# Matrices with Matlab

Given A = [ 2 0 4 B = [ 3 5 2

1 4 -1 0 8 4

3 1 2] 1 0 9]

C = [ 1 D = [ 1 4

2 -2 3]

3]

Respond to the following:

Q21. What is the transpose of A?

Q22. Solve for the determinant of A.

Q23. Calculate the inverse of D.

Q24. What is the product of A x C?

Q25. What is the rank of B?

Q26. Compute the sum of A + B.

Q27. What is the product of 3 x D?

Q28. Calculate the product of C x D.

Q29. Write a set of equations that describe the matrix equation Ax X = C.

Q30. Show that A+B = B+A

Q31. Show that A x B is not equal to B x A.

#### Solution Preview

The following is the output from a MATLAB file used to respond.

initialize matrix

A = [2 0 4; 1 4 -1; 3 1 2];

B = [3 5 2; 0 8 4; 1 0 9];

C = [1; 2; 3];

D = [1 4; -2 3];

transpose of A

Q21 = A'

Q21 =

2 1 3

0 4 1

4 -1 2

Determinant of A

Q22 = det(A)

Q22 =

-26

Inverse of D

Q23 = inv(D)

Q23 =

0.2727 -0.3636

0.1818 0.0909

Product of A x C

Q24 = A*C

Q24 =

14

6

11

Rank of B

Q25 = rank(B)

Q25 =

3

Sum of A+B

Q26 = A+B

Q26 =

5 5 6

1 ...

#### Solution Summary

Performing matrix algebra such as adding and multiplication of matrices.