Question

For which values of a will the following system have no solutions? Exactly one solution? Infinitely many solutions?

x+6y+4z=2
4x+25y+31z=7
2x+13y+(7+a^2)z=-1+a

I tried elimination but that didn't work... I don't know how I would use matricies for this either.

Answer 1

@zepdrix @UnkleRhaukus @saifoo.khan

Answer 2

First, turn it into a matrix!

Answer 3

Umm okay...

Answer 4

Okay.

Answer 5

Here do you understand how I got this?

[1 6 4 2 ]
[4 25 31 7 ]
[2 13 7a^2 -1+a]

Answer 6

Yeah I do.,

Answer 7

Actually it should be 7+ a^2 so

[1 6 4 2 ]
[4 25 31 7 ]
[2 13 7+a^2 -1+a]

OK now do you know how to row reduce this?

Answer 8

Yeah but what about that a?

Answer 9

@BluFoot

Answer 10

We're going to work with that later. It shouldn't get in the way because it's in the bottom row.

Answer 11

I have to still manipulate it like normal correct?

Answer 12

Yes. So first try to get 0s in the first column