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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices3 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.
$\text{B}+\text{C}-2\text{A}$
✓

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{B}+\text{C}-2\text{A}$$\Rightarrow\text{B}+\text{C}-2\text{A}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&-4\end{bmatrix}+\begin{bmatrix}-6&0&0\\0&3&0\\0&0&4\end{bmatrix}-2\begin{bmatrix}2&0&0\\0&-5&0\\0&0&9\end{bmatrix}$
$\Rightarrow\text{B}+\text{C}-2\text{A}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&-4\end{bmatrix}+\begin{bmatrix}-6&0&0\\0&3&0\\0&0&4\end{bmatrix}-\begin{bmatrix}4&0&0\\0&-10&0\\0&0&18\end{bmatrix}$
$\Rightarrow\text{B}+\text{C}-2\text{A}=\begin{bmatrix}1-6-4&0+0-0&0+0-0\\0+0-0&1+3+10&0+0-0\\0+0-0&0+0-0&-4+4-18\end{bmatrix}$
$\Rightarrow\text{B}+\text{C}-2\text{A}=\begin{bmatrix}-9&0&0\\0&14&0\\0&0&-18\end{bmatrix}=\text{diag}\begin{pmatrix}-9&14&-18\end{pmatrix}$

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