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Discrete Math

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I am really stuck on these problems. I've worked a lot of them but I can't get these. Sometimes I

think I know the answer but I can't show how I got it.

1.) Solve each matrix equation for X.
2X + 5A = B

2.) Find the following matrices: a. AB b. BA

A=
2 4
3 1
4 2

B=
3 2 0
-1 -3 5

3.) Find A-1 by forming A|I and then using row operations to obtain I|B, where A-1 = B, check that

AA-1=I and A-1 A = I

A=
2 4 -4
1 3 -4
2 4 -3

4.) Write the system of linear equations represented by the augmented matrix. Use x,y,z and, if

necessary w,x,y and z for the variables.

7 0 4|-3
0 1 -5|11
2 7 0|6

5.) Use Gaussian elimination to find the complete solution to each system of equations, or show that

none exist.

3w + 2x - y + 2z = -12
4w – x + y + 2z = 1
w + x + y + z = -2
-2w + 3x + 2y – 3z = 10

6.) Use Cramer’s rule to solve the system

X – 3y + z = -2
x + 2y = 8
2x – y = 1

7.) Use Cramer’s rule to solve the system

2x + 2y + 3z =10
4x – y + z = -5
5x -2y + 6z = 1

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