Thread: solving a system using A^-1

Let A =

1 0 -1
2 1 -2
0 1 1

find A^-1 of the above matrix using inverse matrices and hence solve the bottom 2 systems:

x - z = 3
2x + y - 2z = 0
y + z = 15

2x - y = 1
3x - y + z = -2
2x - y + z = 3

i got A^-1 =
3 -1 1
-2 1 0
2 -1 1

I solved for system 1, how do I solve for system 2 can you please demonstrate.

Multiply the first equation by -1 and rearrange the system.
2x - y = 1 |*(-1)
3x - y + z = -2
2x - y + z = 3

becomes

3x - y + z = -2
-2x + y = -1
2x - y + z = 3

Then you solve the system like the you solved the first one.