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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\text{A}=\begin{bmatrix}2&3\\5&7\end{bmatrix},\text{ B}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix},\text{C}=\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix},$ find
A + B and B + C
✓

Answer

$\text{A}+\text{B}=\begin{bmatrix}2&3\\5&7\end{bmatrix}+\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}$
It is not possible to add these matrices because the number of elements in A are not equal to the number of elements in B. So, A + B does not exist.
$\Rightarrow\text{B}+\text{C}=\begin{bmatrix}-1&0&2\\3&4&1\end{bmatrix}+\begin{bmatrix}-1&2&3\\2&1&0\end{bmatrix}$
$\Rightarrow\text{B}+\text{C}=\begin{bmatrix}-1-1&0+2&2+3\\3+2&4+1&1+0\end{bmatrix}$
$\Rightarrow\text{B}+\text{C}=\begin{bmatrix}-2&2&5\\5&5&1\end{bmatrix}$

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