Assignment Write a function called odd_index that takes a matrix, M, as input argument and returns a matrix that contains only those elements of M that are in odd rows and columns. In other words, it would return the elements of M at indices (1,1), (1,3), (1,5), …, (3,1), (3,3), (3,5), …, etc. Note that both the row and the column of an element must be odd to be included in the output. The following would not be returned: (1,2), (2,1), (2,2) because either the row or the column or both are even. As an example, if M were a 5- by-8 matrix, then the output must be 3-by-4 because the function omits rows 2 and 4 of M and it also omits columns 2, 4, 6, and 8 of M. 3
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1 Lecture 3 Post-Graduate Students Advanced Programming
(Introduction to MATLAB) Code: ENG 505 Dr. Basheer M. Nasef
Computers & Systems Dept. Problem: Guessing Birth Date 2 The
program can guess your birth date. Run to see how it works.
GuessBirthDate Assignment Write a function called odd_index that
takes a matrix, M, as input argument and returns a matrix that
contains only those elements of M that are in odd rows and columns.
In other words, it would return the elements of M at indices (1,1),
(1,3), (1,5), , (3,1), (3,3), (3,5), , etc. Note that both the row
and the column of an element must be odd to be included in the
output. The following would not be returned: (1,2), (2,1), (2,2)
because either the row or the column or both are even. As an
example, if M were a 5- by-8 matrix, then the output must be 3-by-4
because the function omits rows 2 and 4 of M and it also omits
columns 2, 4, 6, and 8 of M. 3 In the previous lectures 4 Matlab
Windows (workspace, m-file,) Working with Arrays One-Dimensional
Array Two-Dimensional Array Elements of Arrays Built-in Functions
for Arrays Agenda 5 Mathematical Operations with Arrays Addition
and Subtraction. Multiplication. Division: solving systems of
equations Built-in functions to analyze arrays Element by element
operations Generating random values. 6 Matlab has two ways:
1)following linear algebra rules: - Uses the standard symbols: (
*,/,^ ) 2)Element-by-element operations: -Uses the symbols with a
period: (. *,./,.^ ) - These two ways are independent and have
totally different applications. Operations with Arrays 7 The
operations + and are applied where: Arrays have identical size. A
scalar value is added/subtracted to/from an array. Addition and
Subtraction 8 9 10 If A and B are two matrices, the operation A*B
can be carried out only if the number of columns in matrix A is
equal to the number of rows in matrix B. Multiplication 11
Multiplication 12 Multiplication 13 Multiplication 14 We will not
care about the linear algebra rules of arrays division. We just
study the application of such operation in solving a system of
equations. For example: a system of three equations Division 15
Equation solving (using left division): We can also use the
inverse: - To calculate the inverse: Division or 16 Array inverse
17 Array inverse 18 Systems of three equations Solution: First:
write the equations in matrix notation: 19 Systems of three
equations Solution: Second: write Matlab commands: 20 Built-in
Function to Analyze Arrays 21 Built-in Function to Analyze Arrays
22 Built-in Function to Analyze Arrays 23 ELEMENT-BY-ELEMENT
OPERATIONS Useful when we need to perform some mathematical
operation (function) over many quantities. 24 ELEMENT-BY-ELEMENT
OPERATIONS 25 Application: verify a function at different values.
ELEMENT-BY-ELEMENT OPERATIONS 26 This is useful in the simulation
of many physical processes and engineering applications. GENERATION
OF RANDOM NUMBERS The rand command: generates uniformly distributed
random numbers with values between 0 and 1. 27 Generating random
values in a specific range (a,b): GENERATION OF RANDOM NUMBERS 28
GENERATION OF RANDOM NUMBERS Generating random integers : The randi
command: generates uniformly distributed random integers 29
GENERATION OF RANDOM NUMBERS Generating random integers : 30
GENERATION OF RANDOM NUMBERS Generating normally distributed random
values : 31 GENERATION OF RANDOM NUMBERS Generating normally
distributed random values : controlling the standard deviation and
mean by multiplying the number generated by the randn function by
the desired standard deviation, and adding the desired mean. 32
Three forces are applied to a bracket as shown. Determine the total
(equivalent) force applied to the bracket. (A force is a vector (a
physical quantity that has a magnitude and direction) Example 33
Example solution In order to use Matlab we have first to state all
necessary equations and values !. where F is the magnitude of the
force and is its angle relative to the x axis, F x and F y are the
components of F in the directions of the x and y axes, i and j are
unit vectors. If F x and F y are known, then F and can be
determined by: The total (equivalent) force applied on the bracket
is obtained by adding the forces that are acting on the bracket. 34
Example solution m-file: 35 Example solution Result: (in Command
Window) Material & problems 36 We have covered Chapter 3 from
Gilat. Problems you can try: Sample Problem 3-5 (page 85), 1-- 4,
12,13,23,27,31,32
