Question

4. The product y = Ax of an m × n matrix A times a vector x = (x1, x2, . . . , xn) T can be computed row-wise as y = [A(1,:)*x; A(2,:)*x; ... ;A(m,:)*x]; that is y(1) = A(1,:)*x y(2) = A(2,:)*x ... y(m) = A(m,:)*x Write a function M-file that takes as input a matrix A and a vector x, and as output gives the product y = Ax by row, as defined above (Hint: use a for loop to define each entry of the vector y.) Your M-file should perform a check on the dimensions of the input variables A and x and return a message if the dimensions do not match. Call the file myrowproduct.m. Note that this file will NOT be the same as the myproduct.m example. Test your function on a random 5 × 3 matrix A and a random 3 × 1 vector x. Compare the output with A*x. Repeat with a 3 × 6 matrix and a 6 × 1 vector and with a 3 × 6 matrix and a 1 × 6 vector. Use the command rand to generate the random matrices for testing. Include in your lab report the function M-file and the output obtained by running it.

Answer 1

.m file

function y = myrowproduct(A,x)
    y=[];
   [r1 c1]=size(A);
   [r2 c2]=size(x);
    if c1~=r2
       disp('dimensions not agree');
       return;
    else
    for i=1:r1
       y(i,1)=A(i,:)*x;
     end
    end

 end

command window output:

>> clear all
 >> A = [1 2 3;4 5 6]

A =

1 2 3
 4 5 6

>> b = [1;2;3]

b =

1
 2
 3

>> m1 =myrowproduct(A,b)

m1 =

14
 32

>> C = [1 2 3 4;4 5 6 7;2 5 4 7]

C =

1 2 3 4
 4 5 6 7
 2 5 4 7

>> x = [4;2;7;8]

x =

4
 2
 7
 8

>> m1 =myrowproduct(C,x)

m1 =

61
 124
 102

>> x = x'

x =

4 2 7 8

>> m1 =myrowproduct(C,x)

dimensions not agree

m1 =

[]

>>

Let me know if you have any doubts or if you need anything to change. 

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Thank You!
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