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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
A - 2B
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Answer

Given, $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{B}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-\text{b}&3&4\end{pmatrix}$
$\text{A}-2\text{B}$
$=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix}-2\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$
$=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix}-\text{diag}\begin{pmatrix}2&2&-8\end{pmatrix}$
$=\text{diag}\begin{pmatrix}2-2&-5-2&9+8\end{pmatrix}$
$=\text{diag}\begin{pmatrix}0&-7&-17\end{pmatrix}$
So, $\text{A}-2\text{B}=\text{diag}\begin{pmatrix}0&-7&-17\end{pmatrix}$

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