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2a.b.

c.

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O6EC7T

Max. Mark"$100

(04 Marks)

(06 Marks)(04 Marks)

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the minimurn and maximum frame(10 Marks)(04 Marks)(06 Marks)

Seventh Semester B.E. Degree Examination, Dec.2013 lJan.20l4

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Time: 3 hrs.

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PART _ AI a. With la:yer diagram, explain th. ,.rpo.rribFy of each layer in oSI model, (10 Marks)

b. How daiatransfer is achieved using CM and CMIS in CATV channel? (06 Marks)c. Calculate fur minimum time required to download one million bits of information using

Note: Answer FIVEfull questions, selectingat least TWO questions from each part.

With flow diagram, explain.the procedure for CSMA/CD protocol.Explain polling method of controlled access of the channel.

each of the fuUOwing techniques:i) V.32 modemii) V.32 bis modemiii) V.90 modem rl ,, .

What are the different types of framing? Explain bit stuffing with an example. (06 Marks)With design and sliding windo* diagrams, explain Go back - N ARQ protocol. (10 Marks)In a stop and wait ARQ system, the bandwidth-delay product is 20000 bits and 1 bit takes 20ms to make a round trip. What is the B.W. of the line? If the protocol that can send 10frames are 1200 bits in length then what is the percentage of utilizationof the link?10+ Marks)

One hundred stations on a slotted ALOHA network share 1 Mbps channel. If frames are1000 bits long, find the throughput if each station is sending 5 frames/second; (05 Marks)

b.c.

d. Describe the encoding and decoding scheme in CDMA techniques lor channel sharing.(05 Marks)

, "',, " "'

4 a. Explain the frame formats of IEEE 802.3. What arelengths?

b. What are the characteristics of fast Ethernet?c. Desoribe the address mechanism of IEEE 802.11.

- ,,-',,' PART - B5 t-,+l Wlrt is transparent bridge? Explain the process of learning in transparent bridge. (10 Marks)

,, "' ", b. What is VLAN? Explain in detail. What are the advantages of VLAN? (10 Marks)

What is classful addressing in IPV4? What is its mask? Explain. (06 Marks)Find the class of each address:i) 14.23.120.8ii) 252.5.1s.1 1 1

ii, 11000001 10000011 00011011 11111111iv) 00000001 00001011 00001011 11101111

c. What is network address translation (NAT)? Give the NAT imp

I of2

06EC71

(10 Marks)7 a. Explain different forwarding techniques used in network layer.b. Explain the distance vector routing for the graph shown in Fig.eZ(U).r

f'.::.::':::j..,.=%

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L\fp, *".1*g &-- . t8 a. What ar6@Oitterent TCP services and features? Explain them" r*,,,q=* (10 Marks)b. Describe l-lb.F'.-tser datagram format. =;'i

# (06 Marks)::: 6Uc. What are the afrytions of multicast routing? \F*=- iol rvlarrrsy\'lee "

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fu_ u) E-; .\*.4,N. Fig.Q7(b) Topology ofNetwork ,; (10 Marks)'f.,r.=-* - E

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2 of2

USN IOECITET2

Seventh Semester B.E. Degree Examination, Dec.2013 tJan.2ll4,.., . Optical Fiber Gommunication ::

i{=.'fr[me: 3 hrs. Max. Marks:ioo"'.,. ..= Note: Answer FIVEfull questions, selecting ,..'',,,,,,

ni ,t,,* at least TWO questionsfrom eoch part. .'.. , ,,"..,,,,'

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E _., .. PART _ AE 1 a. Desq'ribe block diagram of an optical fiber transmission link and explain:the function of eachS element in link. (08 Marks)

E b. Explain*fut'is meant by graded index optical fiber using simpte.rfi*nlory concept indicate.- g the major advantages of this type of fiber with regard to multimodopropagation. loo naarrs;

$i c. A Graded index fiber with parabolic refractivelndex f,urnr: t.+g urjn, :1.46 if core6-:g i radius is 20 pm. Fhd,the number of modes at 1300nm and lf 50 nm. (06 Marks)Cgu

-h-o ..'Cgu

-h-o -'

.H+ 2 a. Describe Rayleigh Scatti"6ing in optical fiber. (06 Marks).E- ? uwou ruv r\oJ rvrEu ou4lllrldr.rB [r ulJtruar lluEr . i if4: ,:, (ub Marks)

E $ b. Briefly explain intramodal and intermodaldispersion. (06 Marks)E S ':"',,,1:\1f ':::t::' -,,t'tt'z'', ^1a2. \

; ! c. Consider a photodiode with quantum efficiency 75Ya, when photon of energy 1.6x10-roJ,S t are incident on the surface then calculate operating wavelength and it 2.6 pA photo currenta i through detector.coSr€sponding, determine incideni optical p-ower when deiector is operated5 S ^* -^*^ ,..^-.^r^--.L ^

F Pp / .) \; H c. Glass fiber exhibits materiar dispersion gir.; by, r'[ d-'rl

of 0.025. Determine materialtr'tro>9 A dispersion parameter at a wavelength of 0,85 pm and estimate rms pulse broadening / km for

; € good LED source with an rms spee+@id{h of 20 nm at this waveiength. (08 Marks)I

; € 3 a. Sketch and explain Fabry p.rq, ,.ronutor cavity of laser. (07 Marks)

$? b. Discuss rhe operation of ,itb.n RApD *itn n.ltad;;;. eTMarks)

: E c. Consider a photodiod,e;wi,ttri quantum efficiency i5%r-, when photon of energy 1.6x 10-te J.

E * at sarie wavebl$h.'--r ----- o' "''^-*'-l-r *^' svrvvrvr

lr;;;;ag.Eo8" I 4 a. Describg with aid of suitable diagram, three common techniqu" ,3tid6r,-"chanical splicing6 E of optical fibers. (06 Marks)< O l- rrr.rt, , r ^

.

E * b. Wrltt aia of simple sketches, outline major categories of fiber "oupt..r.i E c. A. GaAs optical source that has a refractive index of 3.6 is closelycoupled to

U g b. WitE d of simple sketches, outline major categories of fiber couplers. CI6 Marks)- b c. .lil t aAs optlcal source that has a retracttve rndex of 3.6 is closely coupled to qtrp index fiber=ai ' 'ich has a core refractive index of 1.465, if the source size is smaller than'fibercore, andir* ".Wn-^'o " -^: .,"".::. uqDs vvrw rvuovlrvv lllLte.\ \Jr r.'ruJ, rr ttlg suututr slzg rs slllallcr tnan nDcFcorg, ano

*tWhatisthepowerlossindecibe1sfromsourceintofiber?@X,q#,"t'1=vEE :; > D a nrr! rI //-+-f

^ \Ll \PARr-B /{9"{ _orJh'\o{ E - n: n-.l c.i 5 a. Briefly d,iscuss the possible sources of noise in optical fiber receiffi..*,q[d )g,f;nnu.rrl.g b. Discuss how the eye diagram is powerful measurement tool fod\&stil[gttft da/#dandling2. capability in digital transmission system. \oL*- /r,6ilrvra*jE c. write a note on analog receivers. \Wt06 Marks)Ee'E 6 a. Explain the multi AM techniques employed in broadband analog application. (0E Nrarks)

b. Explain : (i) Microwave photonics (ii) RF over fiber. (06 Marks)c. Explain in brief : (i) Short wavelength band (ii) Chirping. (06 Marks)

I of2

2 of2

USN 06EC73

Seventh Semester B.E. Degree Examination, Dec.20L3 tJan.2ol,A

Power Electronics

E11o.td-E Lcon A*r\3

Note: Answer FIVEfull questions, selectingat least TWO questionsfrom each part.

{,

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i c. Th; #t#; j;;"ii9, temperature of a transistor is T.1 :..-11f0'c and the ambientg temperatur6,isla:25oC. If the thermal impedance are &c :O,$,?.bW, &A: 0.1oC/W and

E s l(sa : O.S"Ci*;tplculate: '.r !B'= ;i the maximum p,ower dissipationo'=

i 5 ii) The case tempefurre. u '-,,1

JhE l,' ur) Also draw the th6r ! equivalent circuit of a transistor. (04 Marks)aT Lal

E i 2 a. Explain switching charactetistics of BJT with models. (06 Marks)E B' b. Explain working with basic-$bflrtur. of OexitdtiOn type n and p channel MOSFETs with

tg ,.f"r"rr..totran-sfercharacteristie." *""' Jr----

(0gMarks)

.g % PARr_Afi I a. Eyl"]ain control characteristic features of the following power devices: (3 ifSqB.. ii) MCT iii) IGBT (r2 Marks)! u lpfueperipheral effects of converters. .,.._''*, 1o+ lvtarhsy

E I c. The base drive circuit in Fig.e2f.)=fruiqt. : 100 V, %, :2.ty, %,: 0.9V, VBE : 0.7y,

= o \/ - 1<\r ^.^l o - 1z n^l^--t^r^-; € VB: 15V and B: 16. Calculate:

H + i) The collector current withMeldmping -=do

= t iil The collector-emitter c$nnu,e voltage Vi".g € vr vrurlrvr v[q*!y}}r6 vvrlqSw y utsi;. ,4,,

F^ = iii) The collector current wglh clamping.&"8E€ # #r; 5 Fig.Q2(c) (06 Marks)bEA f; 3 a. Elpltin turn-on mechanism of a thyristor using two transistor ana{5gy= and derive an

i E rcx@ssion for the anode current in terms of transistor parameters. .. (0s Marks)

iE 9,-.'With the help of neat circuit diagram and waveforms, explain the UJT-triggeri5rg circuit.g ry

': Also mention its advantages over RC triggering. - rio Marks)

* t c. If the latching current for SCR iruerted in between a dc voltage source of 100 V and an=()H f . ut inductance load L:0.1 H is 4 mA. Calculate the minimum width of gate pulse'cfubnt,,1-^-l +^ :------- ^,- -^--^

- - '" rrr vYrsrrr vr bqlw yqrr

5 5; required to turn-on SCR. (02 Marmi==

i"- 4 a. If a converter shown in Fig.Q4(a) has a purely resistive load of R and the delay angle isE .:_r .-

2 a: xl2. Determine: i) 11, ii) Form factor, iii) Ripple factor, iv) TUF, v) PIV ofthyristor.

Fig.Q2(c)

k

4 b' Explain the working of dual converter with a neat circuit diagram. Also obtain waveform forvoltage generating circulating current. (10 Marks)

'':':j - -- .:- 1 r PART-B*oi;rr,,.. 5 ?. MenJion drawbacks of self commutation (any three). (03 Maffir,

" ""','"'"'\, ... b. Explain the operation of complementary commutation with neat circuit and wavefor*r.rffi'':i'" ,. -' , *dy.. equation of c for design consideration. (rlMarks)

'";;'+c' Find the value of C for the commutation circuit shown in Fig.e5(c). Given Ir.*. :t0 A, ton.::::'.,|'': f'of SCRI : 30 psec, E4. : 50 V. Assume 50oZ tolerance on turn-off time. =

"- .

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tt" +, Fig.Q5(c) .j"'r' (05 Marks)

6 a' Explain the working of sirigfu phase bidirectional AC voltage controller for RL loadconsidering discontinuous current flow tlrough load with a nJat circuit and waveforms.Derive equation for vor,or.

,ii:::::::: :: (r0 Marks)b. An ac voltage controller has a resistive igad of R: 10 e and %*": I20y,60 Hz. Thethyristors switch is on for n ; 25 cycles apd off for m : 75 cycles. Determirre: i) Vo.*,,ii) load power, iii) input po-ei factor, iv) Ir"_, .v) Ir*, (10 Marks)

7 a' Explain the principle cf operation of step-down "n"fi$;ti

with a neat circuit and waveform.Derive the equationl&t %"" , %-,, input power * r"nT effective resistance. (10 Marks)

b. Find the *"YI:l efficiency if the load resistance R : i0 Q,lnput supply dc voltage is 220,duty cycle is 50% and chopper voltage drop V.6 :2y. (Converter is ,t.p_ao*r, choiper).

f-rl'. -. (06Marks)c. Draw-1.]i..:'oircuit diagram and waveforms for step-up chopper. -i'-i,,:

(04 Marks)''ttt''"8 ? .E"xqpin current source inverter circuit with waveform. .::..,.!j. (10 Marks)b' .,4"{10 full bridge inverter has resistive load R:2.4 e the dc input voltpge n;":';;Determine: -r --- e -

' .," il RMS output voltage at fundamental frequency.ii) The output power. n't":..\: '':':::: 'irll

'::i

iii) The average and peak current of each transistor. :: ::.'(10 Mrir[q),,.

! .: .,ji::,::::.... -|F

:.t,ir-^, - ru psec, D4s : )U v. Assume )u7o tolerance on turn-off time. t':

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2 of2

USN

Time:3 hrs.

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r0EC74

(08 Marks)

Seventh Semester B.E. Degree Examination, Dec.2013 lJan.201,4

Embedded System DesignI

Note: Answer FrvEfull questions, selecting Max' Marks:100

at least TWO questionsfrom each part. , i

PART-A , ''"

i) Embedded system, ii) Hard RTS, iii) Watch Dog Timer, with an example for(06 Marks)

b.

c.

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Wit[ a:ibbck diagram, explain briefly the various components in 1 miCroprocessor based

embedded*.ystem. ... 'l .ii

(06 Marks)Differentiatb',$etween the two design approaches for an embedded system development.Explain the vang, gllstages with a flow diagram. (08 Marks)

2 a. Compare: . ',,

i) Big Endian and Littie Endian formats.ii) RISC and CISC registers.iii) Truncation and rounding ertors. (06 Marks)

b. Explain direct and register indirept'addrepsihg"inodes with diagrams. Also write the timingdiagram for a serial write operation with an 8 bit register. (06 ivlarks)

c. Write the block diagram of RTN model for a microprocessor data path and memoryinterface. Also explain fetch, exep,utg aiid next control operations with RTL instructions.

3 a. Explain the internal diagram,;of SRAM and writb the timing diagram for read operation.i..i i (06 Marks)

b. Explain associative mappi1rg cache implementation. (06 Marks)c. Write the inside and outSide diagrams for DRAM along with read and write operations. Also

explain refresh operation. (08 Marks)

.1,,,,,,.,. "' ."

,,iir'r.,.4 a. Write the flbw'diagrams for waterfall and V life cycle models artd briefly explain Waterfallsteps. , ' .., .:'. .t|.t,,,,, (06 Marks)

5 a. Diterentiare betrveen'

-

,K"9tr0:ll, i[::H#looi,l,'.',I;, i,{fl",.1l*\$lilt rightweight and heavy weight threads ((il LTBRF*' l: I (06 Marks)

b. Describe: \.\_-.-,{.7i) Reentrant code, \g*Zii) Foreground/background system,iii) Multithreading system. (06 Marks)

b. Explain ,the characteruing and identifuing the requirements of a system with respect to adigital counter. (06 Marks)

c. Write the hardware architecture and data and control flow diagram of a counter system and

,; -;,,explain briefly the flow diagram. (08 Marks)

Describe the task state transition with a diagram and TCB structures. Explain the function ofthe scheduler and also dispatcher. (08 Marks)

I of2

6a,b.

c.

ta.

loE C74

Explain any 6 functions of an operating system in brief. (06 Marks)Describe virtual model and highL level irodel for oS architectures. (06 Marks)write the algorithm for a simple oS Kernel, using c rurgrug" notation for 3 asynchronoustasks using TCBs only. The 3 tasks use a common daia buffer for read, increment anddisplay operations. rvr rvqs' "^-'i;il;.;

write the Amdahl's law limitation for performance improvement/optimization. consider asystem with the following characteristics.i) The task to be improved takes 200 time units and the gral is to reduce the execution timeto 160 time units. The algorithm under considerati"r;;;;d; il;;"r" "Determine

theylpown-narameter vahJ in the equation and write th.l;f.;;;;,*

*"""' 'ii) Ifth{goal is to reduce the execution time to r00 tir"" r;;;;;d; uulr". in case(i), thendeterini4e-the value unknown parameter value in the equatioiffi#ffi# inference.

write a 'c' funciion to determine the sum of the elements.in an ar-ray and, analyzJif ,Hi?line for its time complexityExplain the Big-o nttuti* used for comparing the algorithms, cornmon bounds ,j:: TX'f?

write and analyze a rinear search algorithm for its time complexity. (06 Marks)The operationto beperformed is (i;:c,o u+ b, (iD c: a *.lf u= = belse c: d_e. Write thec language construct and. assembly lungurg. statements for the above 2 cases separately andcalculate the total time required-' if PUSH/pop takes g00 nsec, arithmeticoperation/load/store/cmp takes 400 nsec and the .onJitionut/unconditional branch takes700 nsec.

c.

8a.b.

c' Describe memory roading with equation, figure and an exampre.(06 Marks)(08 Marks)

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2 of2

USN 068,C7 4

(08 Marks)(06 Marks)

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'(O{'Marks)

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(06 Marks)below:

(06 Marks)(04 Marks)

Seventh Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4DSP Algorithms and Architecture

Time: 3 hrs.

i.

Max. Marks:100Note: Answer FIVEfull questions, selecting

atleast TWO questions from each purt.

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a. With a.neht',,,block diagram, explain the scheme of a DSP systemrwith typical signals in aDSP scheme,,,,,. ,:'.,,,

:,. .,..,,.:.. ::::.,,"' (10 Marks)

b. Briefly explain the-,decimation process. :.,, ,:'' .,, (04 Marks)c. An analog signal is"sampled at arate of 8 KHz. If 512 samples of the signal are used to

compute DSP, X(K)l ilelermine the analog and digital frequency spacing between adjacentX(K) elements. Also, determine analog and digital-ftequencies corresponding to K:64.

: :,,,:::, (06 Marks)

a. Investigate to basic features that",should be provided in to DSP architecture to be used toprovided in to DSP architecture to b,ufu$ed to implement to following Nth -order FIR filter.

(06 Marks)b. With a neat diagram, explain trr" ;r;i.;" level parallelism and pipelining with pipelined

implementation of an 8 - tap FIR filter using eight MACs and parallel implementation of an8 - tap FIR filter, using two'MAC units. ,rr' .,';'

c. Explain the indirect addressing mode.'.'rt: .

,,:::':'

a. Explain the maiu'arUhitectural features of TMS 320 C 54 XX processor. (06 Marks)b. Explain the bit'ionfiguration of PMST register. (08 Marks)c. With an ex,ample each, explain immediate addressing mode, absolute addressing mode,

,, , ,,. '''i'""

a- ,. Describe the operation of the following MAC instructions :

;. i,"., MAC x AR 3 +, # 2463 h, A

'i"": MAC * AR 3 -, * AR 5 +, B, A.b. Explain the operations of the following instructions :

MPY*ARZ_,*AR4+O,BSUBxARI+, 14,AsuB # 2345h,9, A, B.Write a program to find the sum of sum of series of signed numbers as specified

4lFh

A - Ir(i)i=4lOh

Assume ARl as pointer to x(i) and AR2 as counter for the numbers.Briefly explain the clock generator of TMS320C54XX.d.

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(08 Marks)(06 Marks)(06 Marks)

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Seventh Semester B.E. Degree Examination, Dec.2013 I Jan.2Ol4Real - Time Systems

Max.

Note: l. Answer ony FIYEfull questions, selecting

t..stleast TWO questionfrom each part.

2. Standars Notations are used.

PART - Aby Real Time systems? Explain the

Technique

What is code sharing? Explain the serially reusable and reentrant code.

Explain software design for RTS using software module.What is the principal difference between pool and channel?

Explain with relevant diagrams, the Ward and Meller method.

Explain Yourdon methodolo gy.

Write a short note on software modeling.

:. .

-=-3..-- a.b.

a.

b.

2a.b.c.

d.

a.

b.

c.

8a.b.c.

c.

4a.

b.

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USN

Time: 3 hrs.

i:

la.

Seventh Semester B.E. Degree Examination, Dec.2013/Jan.2ol4

lmage Processing

06F,,C7s6

(05 Marks)

Max. Marks:100

,,,,,,,,

,..

.

With a neat block diagram, describe various components used in general purpose imageprocessing system. (08 Marks)

Briefly.explain the principle of image formation in Human eye. (08 Marks)Let p dnd q be the pixels at coordinates (5, 5) and (10, 15) respectively. Find out whichdistance',,rneasure gives the minimum distance between the pixels.. . " ,,, (04 Marks)

Explain the pfbeess of image sampling and quantization in arq;lallmage formationlro rvru.t r;

Explain: i) False contouring. iil Checkerboard pattern. (05 Marks)Consider the image se€m€nt shown in Fig.Q2(c). Let V : {2, 3,4}, compute the length ofshortest 4-, 8- and m- path between p and q. If any particular path does not exist between

Note: Answer FIVEfull questions, selectingat least TWO questionsfrom each part.

PART _ A

b.c.

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3 a. Consider a2 x 2transform matrix A and the image U. given below:

^ i[f ;]

2a.

b.

4a.

5a.

(q)

(p)

Calculate the transformed image V and the basis images. Check the image U using basisimages and transformed image V. (10 Marks)Define Haar,transform. Find Haar matrix for N : 8 and explain how it is constructed. Stateits propertids. (10 Marks)

Explaiuthe importance of discrete cosine transform with its equations and properties.

f rrltl LlU=t I

Lr 2)

1r,,, (08 Marks)Write a short note on KL transform. : (06 Marks)Prove that Hadamard transform is a fast transform. (06 Marks)

.PART-B . ii

Consider 8-level grey scale image of size 8 x 8 shown in Fig.Q5(a). Show histogram of t]leimage. Compute equalized hist and display graphically. t"*u*"'"'

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068C756

5 b. Using the second derivative, develop a Laplacian mask for image sharpening. (06 Marks)

c. Exptrain in brief any point processing technique implemented in image processing. (04 Marks)

6 a. Discuss the characteristics of high boost filter for both frequency and spatial domain.

Explain how high boost filtering increases the enhancement of the image..:=

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Wilh the help of block diagram, explain homomorphic filters for image enhancemerl-. _ '

flO1YlaflOlVlarks)dT." .::

tain different image degradation models. flh* (06 Marhsltll ull.l9r9lrt llilaBE us$r4Lr4Lrull lll\r\rvrr. *qf\ " \""in in brief, the inverse filtering approach and its limitations. .E#ft6in how the

lirfri*l&ns can be overcome using Wiener filtering. (10 Marks)

c. WhdSffifu order statistics filter? Explain any one such filter. . fu (04 Marks)

"%- =

\"", .*d38 a. Explain thffi}{pwing color models: .ffi\#

i) RG_B co6*:$del *wii) HSI color nio@= ,..t - (10 Marks)

. - ..' ^^#sff, tlDf gOIOf mOge:: (rr, lvrarrs,

b. Write steps involve=?Ifuonverting colors from HSI to,,$GB. (05 Marks)

c. Explain pseudo color @ge processing in brief. ;.- '' (05 Marks)='*,* *#-J**{ffiuw'

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06ML753USN

Time: 3 hrs.

Seventh Semester B.E. Degree Examination, Dec.2013 lJan.2ol4Linear Algebra

Max. Marks:100

,,:,.: ':::,

[. n '.,'

" l'i',,,\ ,1"''

,r.r1,, '1rl,u

Note: 1. Answer FIVEfull questions, selectingat least TWO questionsfrom each part.

2. Missing data be suitably assumed.!!.,.1S

1

)

3.,,.,.,.

,..

:::

dooLa

C)

6(.)L

E9

GV6oo ll

ioo.=Ndr+

b9pog-c!)

Ez.=oa=

o(.)6O

o0tr6dEb>P,6G-

Ed

-? a)

or=9=o- 6-tro.o Fl'

o=toatE

!o5.e>'hbn"cb0o=sotr>=oo-

lr<- a'.1

ooZ

oa

'/6/'*'o Marks)

t9(/

(10 Marks)

'1.=

Show,that H is aiot'm.r..l

endent inR3?s...1os mar[Si

ff("'*11:\"'. . )ary row operations.

\|***7N.,.>-{qfii\{tgctr',-r,, - .'

--==::f

':;'',rusq':;::

,,: ,,::' ,,

.iit:

space V, let H: span {V1, V2}. Shoi

1) and V:: (1, 5,2)hnearly independe

i) The

valent

, .:$"''

a. ,1""Given: PART - A

It 2 -2 -4 tllt12 4 -3 -6 'lA=13 6 -3 -6 1l

lo B -4 -8 rlttLs l0 -12 -24 8_l

::: --

Find the following: [) The row reduced echelon lorm of A; iiii) Find the general iolution of the system AX: 0.Prove that the following twg matrices are NO'I ro#'equiconditions two matrices are said to be row equivaJent:

lz o ol I-r t 21l" -r ol. l-: I

L; ;'._:l L,',L',l

row rank and nullity of A;(12 Marks)

and mention under what

(08 Marks)

a. Find the inverse of the matrix ,,,,,,

I r 1t2 131ttA:lll2 113 1l 4 | using ihe element

Ll/3 U4 Us)"b. Find an LU factorization of

lz -4 -2 3lI u -e -s 8 I

a:[ a -7 -3 el.I o -2 -2 -rl

T L-6 3 3 4)-,. if Given Vr and Vz are vectors in a vector", subspace ofV.b. Are the vectors Vr : (1, 2,5),Y2: (2,5,

c. Find a basis for col A and a basis for nul A for the given matrixIr 4 8 -3 -71l-, 2 7 3 4lA=l l.l-r 2 9 s s I'[, 6s -s -r)

(10 Marks)

4 a. Determine which of the following functions T from R'+ Bf are linear transformations:i) T(x1, xz) : (xr * xz, xr)i ii) T(x1, x2) : (x1x2, x1). (06 Marks)

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