Vidyalankar EM notes, Chapter: Linear algebra, assignment 7, question 6

Question

Find the eigen values of the matrix and state that whether it is diagonal or not \[
A = \begin{pmatrix}
8 & -8 & -2 \\
4 & -3 & -2 \\
3 & -4 & 1
\end{pmatrix}
\]

options:

A) Eigen value 1, 2, 3 & diagonal

(B) Eigen value 1, 2, 3 and non diagonal

 (C) Eigen value 1, 1, 3 and non diagonal

(D) Eigen value 1, 1, 3 and diagonal

 

I know the answer is either option A or B. My question is does the question ask if the matrix is diagonal or not ? or is it something else?

Answer 1

It's asking whether the Matrix is Diagonalizable or not, that is whether it has a Diagonal matrix or not.
If it is asking this, then yes since Matrix is a square matrix and its eigenvectors will be LI, then it is diagonalizable

But if it is asking whether the matrix itself is diagonal or not. then its not a diagonal matrix