The problem has to do with diagonalizing a square matrix, but the part I'm stuck on is this:
Bx=0, where B is the matrix with rows , [0,-4, 0], and [-3, 0, -4].
After performing rref on the augmented matrix Bl0, I get rows [1,0,4/3,0], [0,1,0,0], .
I am trying now to solve for column vector x=[x1,x2,x3]^transposed.
The Attempt at a Solution
I'm stuck. From every other problem like this I would set x3 = r, where r is an arbitrary constant. x2 has a leading entry and I set that equal to zero, which seems to be the only thing I'm getting correct. I know the answer should be [-4,0,3]^transposed, so x1=-4, x2=0, x3=3 but I can't seem to algebraically get there.
Can someone let me know what I'm missing? Thank you!