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# a) Use Gaussian elimination to find the values of a for the...

a) Use Gaussian elimination to find the values of a for the following equation system to have a solution:

2x + y − 2z = a + 7

3x − y + az = −3

−x + ay − 4z = 8

b) Suppose that **A**, **B **and **C **are three 3 × 3 matrices for which **A **and **B **have inverses. Use the associative and distributive laws of matrix multiplication in order to solve the equation **A**^{-1}(**A **+ **X**)**B** = **C** for **X**.

c) Find |1 3 4| (3*3 matrix) by cofactor expansion along the first row.

| 2 2 1 |

| 3 −3 −9|

Thank you so much!

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