EXPERIMENT NO. 8
Find the inverse of the following matrices by adjacent and sweep
out method:
-347
A)425
751
B)1523
5261
2646
3167
EXPERIMENT NO.
FIND THE RANK OF THE FOLLOWING MATRICES:
3-20-1-7A)02215
1-2-3-21
0121-6
23-11
B)1-1-2-1
313-2
630-7
EXPERIMENT NO. 3
FOR THE FOLLOWING MATRICES FIND THE NON-SINGULAR MATRICES P AND
Q
FORM WHICH PAQ IS IN NORMAL FORM:
A)1-201
2-110
3-311
-1-1-11
3-121B)
14617-11-6172123
EXPERIMENT NO. 13
Solve the following homogeneous equation:
x+3y-2z=0 2x-y+4z=0 x-11y+14z=0
2x+3y-z-t=0 x-y+2z-4t=0 3x+y+3z-4t=0 6x+3y-7t=0
EXPERIMENT NO. 10
Given that
A)112
311
231
B)201
020
102
Show that these matrices satisfy their own characteristic
equation and hence compute their inverses.
EXPERIMENT NO. 14
Solve the following equations after establishing the theory of
consistency:
x+2y-z=3 3x-y+2z=1 2x-2y+3z=2 x-y+z=-1
4x-5y-2z-2=0
5x-4y+2z+2=0 2x+2y+8z-1=0
x+2y-5z+9=0 3x-y+2z-5=0 2x+3y-z-3=0 4x-5y+z+3=0
EXPERIMENT NO. 11
a) Reduce the following matrices to their daigonal form:
231-1 A= 580112-23
123-1B= 4562781072116
Find generalised inverse of a and b by inverting non-singular
minor:
AAGA=AANDBBGB=B
EXPERIMENT NO. 6
A sample survey was conducted to study the yield of wheat and a
sample of 20 farms from a total of 100 was taken with probability
proportional to the area under wheat crop, with replacement method.
The total area under wheat crop was 485.5 hectares. The
observations were as follows:
Area under crop(hectares)Yield of
crops(kgs)5.2285.9293.9304.2224.7224.8254.9286.8374.7265.7325.2255.2384.9314.0161.367.4617.4614.8296.2476.247
Estimate the average yield per farm along with its standard
error. Also estimate the gain due to pps sampling compared to
simple random sampling with replacement.
EXPERIMENT NO. 5
In a village, there are eight orchards. A sample of two orchards
is selected with probability proportional to the number of trees in
the orchards without replacement and the following observations are
recorded:
S.N.NUMBER OFYIELD(Kg)PROBABILITY
TREES(Y)(pi)
(X)
1.26300.096
2.20220.074
Estimate the total production of eight orchards from the above
sample along with standard error by using Des Raj estimator,
Horvitz-Thompson estimator and Murthy unordered estimator.
EXPERIMENT NO. 4
Find the characteristics roots and vectors of the following
matrices:
8-62
A)A =7-4
-6
2-43
3105B)B =-2-3-4
357
6-2-2C)C =-23-1
213
EXPERIMENT NO. 12
Find the basis of row and column null space of the following
matrix:
520-36 A = 123-48-3-621244-1-24
EXPERIMENT NO. 12
EXAMINE WHETHER THE FOLLOWING SET OF VECTORS ARE LINEARLY
INDEPENDENT OR DEPENDENT. IF DEPENDENT, OBTAIN A RELATION
CONNECTING THE VECTORS:
1= (2,1,-2,1), 2= (1,-1,-1,3) , 3= (7,2,-7,4)
1= (1,2,-3,4) , 2= (3,-1,2,1), 3= (1,-5,8,-7)
1= (2,3,-1,-1), 2= (1,-1,-2,-4), 3= (3,1,3,-2), 4=
(0,-2,1,-1)
1= (1,2,-1,3), 2= (0,-2,1,-1), 3= (2,2,-1,5)
EXPERIMENT NO. 15
a) For the given matrix
011-1
A =10-11
1-101
-1110
Find an orthogonal matrix t and a diagonal matrix b such
that
TAT = B
b) Calculate A10
EXPERIMENT NO. 14
REDUCE THE FOLLOWING QUADRATIC FORMS TO CANONICAL FORM. GIVE
ALSO THE REQUIRED LINEAR TRANSFORMATION AND THE NATURE OF THE
QUADRATIC FORM IN EACH CASE:
6x12+3x22+14x32+4x1x2+18x1x2+4x2x3
-21x12+30x1x2-12x1x3-11x22+8x2x3-2x32
x12+x22+4x32+9x42-2x1x2-4x1x2+6x2x4-6x1x4
EXPERIMENT NO. 15
FIND THE LINEAR TRANSFORMATION, WHICH REDUCE THE FOLLOWING
QUADRATIC FORMS:
7x12+10x22+7x32-4x1x2-4x2x3+2x3x1
AND
2x12+3x22+2x32+2x1x3
IN THE FORM
y12+y22+y32
AND
1y12+2y22+3y32
RESPECTIVELY WHERE 1, 2, 3 ARE THE LATENT ROOTS OF THE EQUATION
|A- B| = 0.
