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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:
$3\text{A}-2\text{B}+3\text{C}$
✓

Answer

 Given, $\text{A}=\begin{bmatrix}2&4\\3&2\end{bmatrix},\text{ B}=\begin{bmatrix}1&3\\-2&5\end{bmatrix},\text{ C}=\begin{bmatrix}-2&5\\3&4\end{bmatrix}$

$3\text{A}-2\text{B}+3\text{C}$

$=3\begin{bmatrix}2&4\\3&2\end{bmatrix}-2\begin{bmatrix}1&3\\-2&5 \end{bmatrix}+3\begin{bmatrix}-2&5\\3&4 \end{bmatrix}$

$=\begin{bmatrix}6&12\\9&6\end{bmatrix}-\begin{bmatrix}2&6\\-4&10\end{bmatrix}+\begin{bmatrix}-6&15\\9&12\end{bmatrix}$

$=\begin{bmatrix}6-2-6&12-6+15\\9+4+9&6-10+12\end{bmatrix}$

$=\begin{bmatrix}-2&21\\22&8\end{bmatrix}$

Hence,

$3\text{A}-2\text{B}+3\text{C}=\begin{bmatrix}-2&21\\22&8\end{bmatrix}$ 

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