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Matrices

Matrix equations
A matrix equation is an equation in which a variable stands for a matrix.
You can solve the simpler matrix equations using basic operations. Let's see:

Solve for X A·X=B-C

Where

$\fs2A=\begin{pmatrix}5&-4&1\\3&-3&-1\\-3&2&-2\end{pmatrix}\;,\;B=\begin{pmatrix}5&-5&-2\\-3&4&-4\\-3&-1&-2\end{pmatrix}\;and\;C=\begin{pmatrix}3&5&3\\0&2&-5\\4&0&-1\end{pmatrix}$

X=A-1(B-C)

The inverse matrix of A

$\fs2A^{-1}=\begin{pmatrix}8&-6&7\\9&-7&8\\-3&2&-3\end{pmatrix}$

$\fs2X=\begin{pmatrix}8&-6&7\\9&-7&8\\-3&2&-3\end{pmatrix}$\begin{pmatrix}5&-5&-2\\-3&4&-4\\-3&-1&-2\end{pmatrix}-\begin{pmatrix}3&5&3\\0&2&-5\\4&0&-1\end{pmatrix}$$

$\fs2X=\begin{pmatrix}8&-6&7\\9&-7&8\\-3&2&-3\end{pmatrix}\begin{pmatrix}2&-10&-5\\-3&2&1\\-7&-1&-1\end{pmatrix}$

$\fs2X=\begin{pmatrix}-15&-99&-53\\-17&-112&-60\\9&37&20\end{pmatrix}$

Given

$A=\begin{pmatrix}-3&-3&-2\\-4&3&3\\5&-3&-3\end{pmatrix},\;B=\begin{pmatrix}3&2&6\\6&1&-8\\-8&0&-2\end{pmatrix}\;y\;C=\begin{pmatrix}5&1&3\\2&2&1\\-3&4&-3\end{pmatrix}$

Solve for X: AX+BX=C

 X =