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## Homework Statement

FP1 (MEI June 07)

## Homework Equations

## The Attempt at a Solution

**(i) Find the value of n**

I multiplied the top row of A by the left column of B and got the equation:

-5-16+k=k-n

moved stuff around and ended up with n=21

**(ii)Write down the inverse matrix A**.

^{-1}and write down the conditions on k for this to existWell, I know that k can not be 21 otherwise the determinant will be 0 which cannot be true in this circumstance.

I'm not too sure how to do A

^{-1}. I know that the matrix itself must be what B originally was, but I'm not sure how to find out what k is (and thus the determinant).

**(iii)Using the result from part (ii), or otherwise, solve the following simultaneous equations.**

x-2y+z=1

2x+2y+z=12

3x+2y-z=3

x-2y+z=1

2x+2y+z=12

3x+2y-z=3

I solved this using Gaussian elimination. I know how to solve this using the inverse of matrices, but I couldn't quite do part (ii) so i was unable to use that method.