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 amatrix A and a vector x, and as output gives the product y = Ax byrow, as denoted above (Hint: use a for loop to denote each entry ofthe vector y.) Your M-file should perform a check on the dimensionsof the input variables A and x and return a message if thedimensions do not match. Call the file myrowproduct.m. Note thatthis le will NOT be the same as the myproduct.m example. Test yourfunction on a random 5x2 matrix A and a random 2x1 vector x.Compare the output with A*x. Repeat with a 3x5 matrix and a 5x1vector and with a 3x5 matrix and a 1x5 vector. Use the command randto generate the random matrices for testing. Include in your labreport the function M-file and the output obtained by runningit.
5. Recall that if A is an m n matrix and B is a p q matrix, thenthe product C = AB is denoted if and only if n = p, in which case Cis an m q matrix.
(a) Write a function M-file that takes as input two matrices Aand B, and as output produces the product by columns of the twomatrix. For instance, if A is 3x4 and B is 4x5, the product isgiven by the matrix C = [A*B(:,1), A*B(:,2), A*B(:,3), A*B(:,4),A*B(:,5)]The function file should work for any dimension of A and Band it should perform a
check to see if the dimensions match (Hint: use a for loop todenote each column of C). Call the file columnproduct.m.Test yourfunction on a random 5x3 matrix A and a random 3x5 matrix B .Compare the output with A*B. Repeat with 3 x 6 and 6 x 4 matricesand with 3 x 6 and 4 x 6 matrices.Use the command rand to generatethe random matrices for testing. Include in your lab report thefunction M-file and the output obtained by running it.
(b) Write a function M- file that takes as input two matrices Aand B, and as output produces the product by rows of the twomatrices. For instance, if A is 3 x 4 and B is 4x5, the product ABis given by the matrix C = [A(1,:)*B; A(2,:)*B; A(3,:)*B] Thefunction file should work for any dimension of A and B and itshould perform a check to see if the dimensions match (Hint: use afor loop to denote each row of C). Call the file rowproduct.m. Testyour function on a random 5x3 matrix A and a random 3x5 matrix B .Compare the output with A*B. Repeat with 3 x 6 and 6 x 4 matricesand with 3 x 6 and 4 x 6 matrices. Use the command rand to generatethe random matrices for testing.
Include in your lab report the function M-file and the outputobtained by running it.
