Hi guys, I'm hoping you can help me. I'm sure I've done something wrong, though I can't figure out what. The question I have to answer is this:
Find invertible U and diagonal D such that . A is the matrix:
2, -4, 2
-4, 2, -2
2, -2, -1
I have found the three eigenvalues -2, -2, 7. I understand that these values, along the diagonal of a matrix otherwise filled with zeros, make up the D matrix.
I have also found the eigenvectors that go with the eigenvalues. Respectively they are [0,1,2], [1,0,-2], [1,-1,1/2]. I understand that these three vectors together make up U.
My problem is how to fit it all together. I don't understand what order I have to put the vectors in within U, or the values in within D, to prove that . I've tried to brute force it but I'm not getting anywhere and it's making me think I've done everything wrong.
Can anyone explain my mistake, please?