Question

q) matrix x such that?
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Answer 1

STEPS:

$\begin{pmatrix}1&2&3\\ 2&3&2\\ 1&2&2\end{pmatrix}X=\begin{pmatrix}2&2&-5\\ -2&-1&4\\ 1&0&-1\end{pmatrix}$

$\mathrm{Multiply\:both\:sides\:of\:the\:equation\:by}\:\begin{pmatrix}1&2&3\\ 2&3&2\\ 1&2&2\end{pmatrix}^{-1}\:\mathrm{from\:the\:left}$

$AX=B\quad \Rightarrow \quad \:X=A^{-1}B$

$X=\begin{pmatrix}1&2&3\\ 2&3&2\\ 1&2&2\end{pmatrix}^{-1}\begin{pmatrix}2&2&-5\\ -2&-1&4\\ 1&0&-1\end{pmatrix}$

$\begin{pmatrix}1&2&3\\ 2&3&2\\ 1&2&2\end{pmatrix}^{-1}\begin{pmatrix}2&2&-5\\ -2&-1&4\\ 1&0&-1\end{pmatrix}=\begin{pmatrix}-5&2&3\\ 2&-3&2\\ 1&2&-4\end{pmatrix}$

$\begin{pmatrix}1&2&3\\ 2&3&2\\ 1&2&2\end{pmatrix}^{-1}\begin{pmatrix}2&2&-5\\ -2&-1&4\\ 1&0&-1\end{pmatrix}=\begin{pmatrix}-5&2&3\\ 2&-3&2\\ 1&2&-4\end{pmatrix}$

Ans: $X=\begin{pmatrix}-5&2&3\\ 2&-3&2\\ 1&2&-4\end{pmatrix}$

if you want to see the extended steps for the question, here's a link i am giving here: https://www.symbolab.com/solver/matrix-calculator/%5Cbegin%7Bpmatrix%7D1%262%263%5C%5C%202%263%262%5C%5C%201%262%262%5Cend%7Bpmatrix%7DX%3D%5Cbegin%7Bpmatrix%7D2%262%26-5%5C%5C%20-2%26-1%264%5C%5C%201%260%26-1%5Cend%7Bpmatrix%7D