# Find the values of m and k so that begin{bmatrix}1 & -2 m & 3 end{bmatrix} cdot begin{bmatrix}k & 0&2 -1 & 3 & 4 end{bmatrix} = begin{bmatrix}3 & -6&-6 -1 & 9 & 16 end{bmatrix}

Find the values of m and k so that
$\left[\begin{array}{cc}1& -2\\ m& 3\end{array}\right]\cdot \left[\begin{array}{ccc}k& 0& 2\\ -1& 3& 4\end{array}\right]=\left[\begin{array}{ccc}3& -6& -6\\ -1& 9& 16\end{array}\right]$
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Step 1
According to the given information, it is required to determine the values of m and n. $\left[\begin{array}{cc}1& -2\\ m& 3\end{array}\right]\cdot \left[\begin{array}{ccc}k& 0& 2\\ -1& 3& 4\end{array}\right]=\left[\begin{array}{ccc}3& -6& -6\\ -1& 9& 16\end{array}\right]$
Step 2
First multiply the matrices.
$\left[\begin{array}{cc}1& -2\\ m& 3\end{array}\right]\cdot \left[\begin{array}{ccc}k& 0& 2\\ -1& 3& 4\end{array}\right]=\left[\begin{array}{ccc}1\left(k\right)+\left(-2\right)\left(-1\right)& 1\left(0\right)+\left(-2\right)\left(3\right)& 1\left(2\right)+\left(-2\right)\left(4\right)\\ mk-3& 0+3\left(3\right)& 2m+12\end{array}\right]$
$\left[\begin{array}{cc}1& -2\\ m& 3\end{array}\right]\cdot \left[\begin{array}{ccc}k& 0& 2\\ -1& 3& 4\end{array}\right]=\left[\begin{array}{ccc}k+2& -6& -6\\ mk-3& 9& 2m+12\end{array}\right]$
Step 3
Two matrices are equal if their corresponding entries are equal.
$A=B⇒{a}_{ij}={b}_{ij}$
$\left[\begin{array}{ccc}k+2& -6& -6\\ mk-3& 9& 2m+12\end{array}\right]=\left[\begin{array}{ccc}3& -6& -6\\ -1& 9& 16\end{array}\right]$
so,
$k+2=3$
$k=1$
$2m+12=16$
$2m=4$
$m=2$
Jeffrey Jordon