# Tagged: defective matrix

## Quiz 13 (Part 1) Diagonalize a Matrix

## Problem 385

Let

\[A=\begin{bmatrix}

2 & -1 & -1 \\

-1 &2 &-1 \\

-1 & -1 & 2

\end{bmatrix}.\]
Determine whether the matrix $A$ is diagonalizable. If it is diagonalizable, then diagonalize $A$.

That is, find a nonsingular matrix $S$ and a diagonal matrix $D$ such that $S^{-1}AS=D$.

## How to Diagonalize a Matrix. Step by Step Explanation.

## Problem 211

In this post, we explain how to diagonalize a matrix if it is diagonalizable.

As an example, we solve the following problem.

Diagonalize the matrix

\[A=\begin{bmatrix}

4 & -3 & -3 \\

3 &-2 &-3 \\

-1 & 1 & 2

\end{bmatrix}\]
by finding a nonsingular matrix $S$ and a diagonal matrix $D$ such that $S^{-1}AS=D$.

(Update 10/15/2017. A new example problem was added.)

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