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Diagonalize $$$\left[\begin{array}{cc}\frac{5}{2} & \frac{3}{2}\\- \frac{3}{2} & - \frac{1}{2}\end{array}\right]$$$

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

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Your Input

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

Solution

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

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

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.


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