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Solve the following.
If (2 3; 5 7) (1 -3; -2 4) = (-4 6; -9 x), find x.
If $\begin{pmatrix} 2 & 3 \\ 5 & 7 \end{pmatrix} \begin{pmatrix} 1 & -3 \\ -2 & 4 \end{pmatrix} = \begin{pmatrix} -4 & 6 \\ -9 & x \end{pmatrix}$, find $x$.
Answer
Answer
Multiplying, the element in row 2, column 2 is $5(-3) + 7(4) = -15 + 28 = 13$.
Check: $2-6=-4$, $-6+12=6$, $5-14=-9$ all match.
Final answer: $13$