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Diagonalize [5232−32−12]\left[\begin{array}{cc}\frac{5}{2} & \frac{3}{2}\\- \frac{3}{2} & - \frac{1}{2}\end{array}\right]

The calculator will diagonalize (if possible) the square 22x22 matrix [5232−32−12]\left[\begin{array}{cc}\frac{5}{2} & \frac{3}{2}\\- \frac{3}{2} & - \frac{1}{2}\end{array}\right], with steps shown.
A

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Your Input

Diagonalize [5232−32−12]\left[\begin{array}{cc}\frac{5}{2} & \frac{3}{2}\\- \frac{3}{2} & - \frac{1}{2}\end{array}\right].

Solution

First, find the eigenvalues and eigenvectors (for steps, see eigenvalues and eigenvectors calculator).

Eigenvalue: 11, eigenvector: [−11]\left[\begin{array}{c}-1\\1\end{array}\right].

Since the number of the eigenvectors is less than the dimension of the matrix, the matrix is not diagonalizable.

Answer

The matrix is not diagonalizable.