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# The following problem, two matrices A and B and two numbers c and d are given. Compute the matrix cA + dB.$\mathbf{A}=\left[\begin{array}{rrr} 2 & 0 & -3 \\ -1 & 5 & 6 \end{array}\right], \mathbf{B}=\left[\begin{array}{rrr} -2 & 3 & 1 \\ 7 & 1 & 5 \end{array}\right], c=5, d=-3$

Solution

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$cA+dB=\\\\\\ =5\begin{bmatrix} 2&0&-3 \\ -1&5 &6 \end{bmatrix}-3\begin{bmatrix} -2&3&1 \\ 7& 1&5 \end{bmatrix}=\\\\\\ =\begin{bmatrix} 10&0&-15 \\ -5&25 &30 \end{bmatrix}-\begin{bmatrix} -6&9&3 \\ 21& 3&15 \end{bmatrix}=\\\\\\ =\begin{bmatrix} 10-(-6)&0-9&-15-3 \\ -5-21&25-3 &30-15 \end{bmatrix}=\\\\\\ =\begin{bmatrix} 16&-9&-18 \\ -26&22 &15 \end{bmatrix}$

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