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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Let $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix}$ and $\text{C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}.$ Find each of the following:
$2\text{A}-3\text{B}$
✓

Answer

Given, $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{ B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix},\text{ C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}$
$2\text{A}-3\text{B}$
$=2\begin{bmatrix}2&4\\3&2\end{bmatrix}-3\begin{bmatrix}1&3\\-2&5 \end{bmatrix}$
$=\begin{bmatrix}4&8\\6&4\end{bmatrix}-\begin{bmatrix}3&9\\-6&15 \end{bmatrix}$
$=\begin{bmatrix}4-3&8-9\\6+6&4-15\end{bmatrix}$
$=\begin{bmatrix}1&-1\\12&-11\end{bmatrix}$
Hence,
$2\text{A}-3\text{B}=\begin{bmatrix}1&-1\\12&-11\end{bmatrix}$

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