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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices3 Marks
Question
Let $\text{A}=\begin{bmatrix}-1&0&2\\3&1&4 \end{bmatrix},\text{ B}=\begin{bmatrix}0&-2&5\\1&-3&1 \end{bmatrix}$ and $\text{C}=\begin{bmatrix}1&-5&2\\6&0&-4 \end{bmatrix}.$ Compute 2A - 3B + 4C.
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Answer

Here,
$2\text{A}-3\text{B}+4\text{C}=2\begin{bmatrix}-1&0&2\\3&1&4\end{bmatrix}-3\begin{bmatrix}0&-2&5\\1&-3&1\end{bmatrix}+4\begin{bmatrix}1&-5&2\\6&0&-4\end{bmatrix}$
$\Rightarrow2\text{A}-3\text{B}+4\text{C}=\begin{bmatrix}-2&0&4\\6&2&8\end{bmatrix}-\begin{bmatrix}0&-6&15\\3&-9&3\end{bmatrix}+\begin{bmatrix}4&-20&8\\24&0&-16\end{bmatrix}$
$\Rightarrow2\text{A}-3\text{B}+4\text{C}=\begin{bmatrix}-2-0+4&0+6-20&4-15+8\\6-3+24&2+9+0&8-3-16\end{bmatrix}$
$\Rightarrow2\text{A}-3\text{B}+4\text{C}=\begin{bmatrix}2&-14&-3\\27&11&-11\end{bmatrix}$

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