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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Find a matrix X such that 2A + B + X = 0, where.
$\text{A}=\begin{bmatrix}-1&2\\3&4\end{bmatrix},\text{B}=\begin{bmatrix}3&-2\\1&5\end{bmatrix}$
✓

Answer

Given: $\text{A}=\begin{bmatrix}-1&2\\3&4\end{bmatrix},\text{B}=\begin{bmatrix}3&-2\\1&5\end{bmatrix}$
and
$2\text{A}+\text{B}+\text{x}=0$
$\Rightarrow\text{x}=-2\text{A}-\text{B}$
$\Rightarrow\text{x}=-2\begin{bmatrix}-1&2\\3&4\end{bmatrix}-\begin{bmatrix}3&-2\\1&5\end{bmatrix}$
$\Rightarrow\text{x}=\begin{bmatrix}2&-4\\-6&-8\end{bmatrix}-\begin{bmatrix}3&-2\\1&5\end{bmatrix}$
$\Rightarrow\text{x}=\begin{bmatrix}2-3&-4+2\\-6-1&-8-5\end{bmatrix}$
$\Rightarrow\text{x}=\begin{bmatrix}-1&-2\\-7&-13\end{bmatrix}$
Hence,
$\text{x}=\begin{bmatrix}-1&-2\\-7&-13\end{bmatrix}$

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