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

$\fs2A=\left(\begin{matrix}-1&1&0\\3&0&5\\5&-3&3\end{matrix}\right)\;,\;B=\left(\begin{matrix}1&1&3\\4&0&5\\-3&-5&-4\end{matrix}\right)\;and\;C=\left(\begin{matrix}0&-5&1\\3&-3&-3\\1&5&2\end{matrix}\right)$

X=A^-1(B-C)

The inverse matrix of A

$\fs2A^{-1}=\left(\begin{matrix}15&-3&5\\16&-3&5\\-9&2&-3\end{matrix}\right)$

$\fs2X=\left(\begin{matrix}15&-3&5\\16&-3&5\\-9&2&-3\end{matrix}\right)\[\left(\begin{matrix}1&1&3\\4&0&5\\-3&-5&-4\end{matrix}\right)-\left(\begin{matrix}0&-5&1\\3&-3&-3\\1&5&2\end{matrix}\right)\]$

$\fs2X=\left(\begin{matrix}15&-3&5\\16&-3&5\\-9&2&-3\end{matrix}\right)\left(\begin{matrix}1&6&2\\1&3&8\\-4&-10&-6\end{matrix}\right)$

$\fs2X=\left(\begin{matrix}-8&31&-24\\-7&37&-22\\5&-18&16\end{matrix}\right)$

Given

$A=\left(\begin{matrix}2&4\\-4&-4\end{matrix}\right),\;B=\left(\begin{matrix}-5&-2\\8&1\end{matrix}\right)\;y\;C=\left(\begin{matrix}-4&-1\\0&-2\end{matrix}\right)$

Solve for X: AX+BX=C

X =