Question

Review: Diagonalization.

Give me some time to put the question and my solution. I got a different answer, so I need help correcting my solution.

Answer 1

Oh, I was about to say, yo wheres da question at XD

Answer 2

Show that A is diagonalizable then diagonalize A (that is, find an invertible matrix P and diagonal matrix D such that \(\sf P^{-1}AP=D\))



My solution:
• Attachment 1: I found the eigenvalues, to know the algebraic multiplicity
• Attachment 2: Next, eigenvectors, to know the geometric multiplicity

So since algebraic multiplicity= geometric multiplicy, A is diagonalizable.

• Attachment 3: I used the eigenvectors I got as my P matrix. I formed 3 x3 matrix, so it should be invertible. Then, I calculated for P inverse using \(\sf \frac{1}{det(P)} (cof(P))^T\) ( we are not allowed to use \(\sf P^{-1}P=I\) )

Lastly, I used \(\sf P^{-1}AP=D\) to diagonalize A... but I think I made a mistake somewhere since I got a different answer.