QQuestion
If A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}, B = \begin{bmatrix}2 & 1 \\ 4 & 2\end{bmatrix} and C = \begin{bmatrix}-5 & 1 \\ 7 & -4\end{bmatrix}, find:
(a) A + C
(b) B(A + C)
(c) 5B
(d) B(A + C) − 5B
ICSEClass XMathematicsMatrices05 Mark2025 Hard
✓Answer
(a) \mathrm{A}+\mathrm{C}=\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}+\begin{bmatrix}-5 & 1 \\ 7 & -4\end{bmatrix}
=\begin{bmatrix}1-5 & 2+1 \\ 3+7 & 4-4\end{bmatrix}=\begin{bmatrix}-4 & 3 \\ 10 & 0\end{bmatrix}(b) \mathrm{B}(\mathrm{A}+\mathrm{C})=\begin{bmatrix}2 & 1 \\ 4 & 2\end{bmatrix}\begin{bmatrix}-4 & 3 \\ 10 & 0\end{bmatrix}
=\begin{bmatrix}(2\times-4)+(1\times10) & (2\times3)+(1\times0) \\ (4\times-4)+(2\times10) & (4\times3)+(2\times0)\end{bmatrix} =\begin{bmatrix}2 & 6 \\ 4 & 12\end{bmatrix}(c) 5\mathrm{B}=5\begin{bmatrix}2 & 1 \\ 4 & 2\end{bmatrix}=\begin{bmatrix}10 & 5 \\ 20 & 10\end{bmatrix}
(d) \mathrm{B}(\mathrm{A}+\mathrm{C})-5\mathrm{B}=\begin{bmatrix}2 & 6 \\ 4 & 12\end{bmatrix}-\begin{bmatrix}10 & 5 \\ 20 & 10\end{bmatrix}
=\begin{bmatrix}-8 & 1 \\ -16 & 2\end{bmatrix}Was this answer helpful?
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