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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
Question
If $3\text{A}-\text{B}=\begin{bmatrix}5 & 0 \\1 & 1 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}4 & 3 \\2 & 5 \end{bmatrix},$ then find the matrix A.
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Answer

$3\text{A}-\text{B}=\begin{bmatrix}5 & 0 \\1 & 1 \end{bmatrix}$
We need to calculate A.
$3\text{A}=\begin{bmatrix}5 & 0 \\1 & 1 \end{bmatrix}+\text{B}$
$\therefore\ \text{B}=\begin{bmatrix}4 & 3 \\2 & 5 \end{bmatrix}\ \ (\text{given})$
$3\text{A}=\begin{bmatrix}9 & 3 \\3 & 6 \end{bmatrix}$
$\text{A}=\frac{1}{3}\begin{bmatrix}9 & 3 \\3 & 6 \end{bmatrix}$
$\text{A}=\begin{bmatrix}3 & 1 \\1 & 2 \end{bmatrix}$

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