FIRST LET ME SAY: I would like to be able to do this problem for myself, so if you want to actually do the problem, please don't post the answer right away so I can try it myself first.

The problem is: suppose the vector x =

[1

0

2]

and A is a (3x3) matrix such that (Atranspose)(A)(x) =

[2

2

0]

what is || Ax || ^2

So far I'm pretty much completely lost. I was thinking I could set (Atranspose)(A) equal to C and then solve for Cx=[2,2,0] but to be honest I wasn't sure even how to do that. I know that if x had been a square matrix I could have multiplied both sides by the inverse of x but obviously x isn't a square matrix.

Help please!