Question

The matrix A=[-2 2 -3 2 1 -6 -1 -2 0] has an eigen value 5 with corresponding eigen vector X=[1 2 -1].Find A^5X.

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Answer 1

Step-by-step explanation:

Can a matrix have infinite eigenvectors

Answer 2

Given:

$A=\left[\begin{array}{ccc}-2&2&-3\\2&1&-6\\-1&-2&0\end{array}\right]$

$X=\left[\begin{array}{ccc}1&2&-1\end{array}\right]$

To find: $A^{5} X$

Step-by-step explanation:

Step 1 of 2

$A^{5} =\left[\begin{array}{ccc}-2&2&-3\\2&1&-6\\-1&-2&0\end{array}\right]^{5}\\A^{5} =\left[\begin{array}{ccc}178&842&-1263\\842&1441&-2526\\-421&-842&1020\end{array}\right]$

Step 2 of 2

$A^{5} X=\left[\begin{array}{ccc}178&842&-1263\\842&1441&-2526\\-421&-842&1020\end{array}\right]\left[\begin{array}{ccc}1&2&-1\end{array}\right]\\A^{5} X=\left[\begin{array}{ccc}2283&4566&7335\end{array}\right]$

Therefore, $A^{5} X=\left[\begin{array}{ccc}2283&4566&7335\end{array}\right]$