Diagonalizing a 2×2 matrix with eigenvalues -4 and 1

[939]

Homework Statement

I am pretty sure I went completely wrong but not sure where. Please help!

2 -3
2 -5

Homework Equations

2 -3
2 -5

The Attempt at a Solution

(note: I apologize for poor notation)

eigenvalues = -4, 1
eigenvectors = (1/√5)(1/2), (1/√10)(3/1)

The matrix is not symmetric, thus the diagonal is (Q^-1)(A)(Q) = λ

 

[HallsofIvy]

What you have done looks good but your last line is not at all clear. You have not said what "Q" is. $Q^{-1}AQ$ is a 2 by 2 matrix, not a "diagonal", and you have not said what "$\lambda$" is intended to mean. Your attachment is correct.