Thread: Finding matrices with a given eigenvector/eigenvalue

Problem: Find all 2x2 matrices for which is an eigenvector with associated eigenvalue -1.

Here's my attempt:











This is where I start to get off track, assuming I was actually on the correct track. A push in the right direction would be great.

Thanks.

Originally Posted by tangibleLime

Problem: Find all 2x2 matrices for which is an eigenvector with associated eigenvalue -1.

Here's my attempt:











This is where I start to get off track, assuming I was actually on the correct track. A push in the right direction would be great.

Thanks.

One hundred percent correct, actually! Just solve those last two simultaneous equations!

2a+3b=-2

b=-(2a+2)/3

2c+3d=-3

d=-(2c+3)/3

Huzzah! Thanks, I got it.

And thanks to alexmahone for confirming my answer.