Solving a Matrix System: a^2 - 1, a, b

[lolimcool]

hey anyone want to help me start solving this matrix for a b c d where the system will be consistent

[1 -2 4 | 7 ]
[0 (a^2 - 1) a | 3 ]
[0 0 b | -3]

 

[micromass]

You can start by transforming this matrix back into a system of equations of x, y, z. What system do you obtain?

 

[lolimcool]

x -2y + 4z = 7
0 (a^2 -1)y + az = 3
bz = -3

 

[Hurkyl]

What does it mean to be consistent? It means that you can solve it, right? ...

 

[lolimcool]

yeah, i know I've tried to solve it, just keep getting stuck

 

[micromass]

What does z need to be in order to be consistent? (look at the last equation!)

 

[lolimcool]

cant z be either -1, 1, 3, -3 ?