Lennie Carroll

2020-12-09

Given the matrices A and B shown below , solve for X in the equation $-\frac{1}{3}X+\frac{1}{2}A=B$
$A=\left[\begin{array}{cc}-10& 4\\ 8& 8\end{array}\right],B=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]$

StrycharzT

Expert

Step 1
the given matrices are:
$A=\left[\begin{array}{cc}-10& 4\\ 8& 8\end{array}\right],B=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]$
we have to solve for X in the equation $-\frac{1}{3}X+\frac{1}{2}A=B$
Step 2
the given matrices are:
$-\frac{1}{3}X+\frac{1}{2}A=B$
$\frac{-1}{3}X+\frac{1}{2}\left[\begin{array}{cc}-10& 4\\ 8& 8\end{array}\right]=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]$
$\frac{-1}{3}X+\left[\begin{array}{cc}-\frac{10}{2}& \frac{4}{2}\\ \frac{8}{2}& \frac{8}{2}\end{array}\right]=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]$
$\frac{-1}{3}X+\left[\begin{array}{cc}-5& 2\\ 4& 4\end{array}\right]=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]$
$\frac{-1}{3}X=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]-\left[\begin{array}{cc}-5& 2\\ 4& 4\end{array}\right]$
$\frac{-1}{3}X=\left[\begin{array}{cc}9& -1\\ 4& 2\end{array}\right]+\left[\begin{array}{cc}5& -2\\ -4& -4\end{array}\right]$
$\frac{-1}{3}X=\left[\begin{array}{cc}9+5& -1-2\\ 4-4& 2-4\end{array}\right]$
$\frac{-1}{3}X=\left[\begin{array}{cc}14& -3\\ 0& -2\end{array}\right]$
$X=-3\left[\begin{array}{cc}14& -3\\ 0& -2\end{array}\right]$
$X=\left[\begin{array}{cc}14×\left(-3\right)& -3×\left(-3\right)\\ 0×\left(-3\right)& -2×\left(-3\right)\end{array}\right]$
$X=\left[\begin{array}{cc}-42& 9\\ 0& 6\end{array}\right]$
Step 3
therefore the matrix X is $\left[\begin{array}{cc}-42& 9\\ 0& 6\end{array}\right]$
therefore the solution of X for the equation

Jeffrey Jordon

Expert