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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Compute the indicated products:
$\begin{bmatrix}2&3&4\\3&4&5\\4&5&6\end{bmatrix}\begin{bmatrix}1&-3&5\\0&2&4\\3&0&5\end{bmatrix}$
✓

Answer

$\begin{bmatrix}2&3&4\\3&4&5\\4&5&6\end{bmatrix}\begin{bmatrix}1&-3&5\\0&2&4\\3&0&5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2\times1+3\times0+4\times3&2\times(-3)\times2+4\times0&2\times5+3\times4+4\times5\\3\times1+4\times0+5\times3&3\times(-3)+4\times2+5\times0&3\times5+4\times4+5\times5\\4\times1+5\times0+6\times3&4\times(-3)+5\times2+6\times0&4\times5+5\times4+6\times5\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2+0+12&-6+6+0&10+12+20\\3+0+15&-9+8+0&15+16+25\\4+0+18&-12+10+0&20+20+30\end{bmatrix}$
$\Rightarrow\begin{bmatrix}14&0&42\\18&-1&56\\22&-2&70\end{bmatrix}$

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