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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}1&2\\3&4 \end{bmatrix}\begin{bmatrix}3&1\\2&5 \end{bmatrix}=\begin{bmatrix}7&11\\\text{k}&23 \end{bmatrix},$ then write the value of k.
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Answer

Given: $\begin{bmatrix}1&2\\3&4 \end{bmatrix}\begin{bmatrix}3&1\\2&5 \end{bmatrix}=\begin{bmatrix}7&11\\\text{k}&23 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}3+4&1+10\\9+8&3+20 \end{bmatrix}=\begin{bmatrix}7&11\\\text{k}&23 \end{bmatrix}$
$\Rightarrow\begin{bmatrix}7&11\\17&23 \end{bmatrix}=\begin{bmatrix}7&11\\\text{k}&23 \end{bmatrix}$
The corresponding elements of two equal matrices are equal.
$\therefore$ k = 17

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