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Algebra of Matrices — MATHS STD 12 Science — Question

Rajasthan 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:
$3\text{A}-\text{C}$
✓

Answer

Given, $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{ B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix},\text{ C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}$
$3\text{A}-\text{C}$
$\Rightarrow3\text{A}-\text{C}=3\begin{bmatrix}2&4\\3&2\end{bmatrix}-\begin{bmatrix}-2&5\\3&4 \end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}6&12\\9&6\end{bmatrix}-\begin{bmatrix}-2&5\\3&4 \end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}6+2&12-5\\9-3&6-4\end{bmatrix}$
$\Rightarrow3\text{A}-\text{C}=\begin{bmatrix}8&7\\6&2\end{bmatrix}$

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