Question

A = [5 2 -4 2 5 -4 4 4 -5]Is A diagonalizable? Why or why not? a. A is diagonalizable because if you just chop off the upper and lower triangles of the matrix, you're left with just the diagonal, so it just got diagonalized. Bayum! b. A is not diagonalizable because it is not a diagonal matrix c. A is diagonalizable because αA(λ) = γA(λ) for all eigenvalues of λ.d. A is diagonalizable because it is a square matrix.e. A is not diagonalizable because αA(λ) ≠ γA(λ) for all eigenvalues of λ.f. A is not diagonalizable because it does not have 3 distinct eigenvalues

Answer 1

A is diagonalizable because αA(λ) = γA(λ) for all eigenvalues of λ. ( C )

Explanation:

The matrix

`A = \left[\begin{array}{ccc}5&2&-4\\2&5&-4\\4&4&-5\end{array}\right]`

This is a 3 x 3 matrix

Attached below is the prove that A is diagonalizable