&nbsp;Find a&nbsp;3&times;33&times;3&nbsp;matrix&nbsp;AA&nbsp;such that&nbsp;Ax⃗&nbsp;=9x⃗&nbsp;Ax&rarr;=9x&rarr;&nbsp;for all&nbsp;x⃗&nbsp;x&rarr;&nbsp;in&nbsp;R&nbsp;

Find a 3x3 matrix A such that Ax⃗ =9x⃗ for all x⃗ in R
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nick1337

$Ax=9x$

Consider the matrix $3×3$

$=\left[\begin{array}{ccc}9& 0& 0\\ 0& 9& 0\\ 0& 0& 9\end{array}\right]$

for all $x$ in $A$

Since

this equals $0$ for all values of $x$