1.

Determine matrix C given by the following expression

if matrices A and B are

2.

Find the product AB and BA for the matrices of Problem 1.

3.

Show that the product AB of the following rectangular matrices is a singular matrix:

4.

Let

1. Compute AB and BA and show that AB ? BA.

2. Find (A+B)+C and A+(B+C).

3. Show that (AB) ^T= B ^T A ^T .

5.

Let

then show that (AB) ^?1= B ^?1 A ^{? 1} .

6.

Find a value of x and a value of y so that AB ^T=0, where A=[1 x 1] and B=[ ?2 2 y].

7.

Evaluate the determinant of each matrix

8.

Find all zeros (values of x such that f(x)=0) of the polynomial f(x)= det (A), where

9.

Compute the adjoint of each matrix A, and find the inverse of it if it exists

1. ,

2. ,

3. .

10.

Let

Show that A(Adj A)= (Adj A)A=det (A) I ₃.

11.

Use the matrices of Problem 9 and solve the following systems using the matrix inverse method

1. A x=[1, 1] ^T,

2. A x=[2, 1, 3] ^T, and

3. A x=[1, 0, 1] ^T.

12.

Solve the following systems using the matrix inverse...