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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
If $\begin{bmatrix}2\text{x}+1&5\text{x}\\0&\text{y}^2+1\end{bmatrix}=\begin{bmatrix}\text{x}+3&10\\0&26\end{bmatrix},$ find the value of (x + y).
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Answer

As the given matrices are equal, therefore, their corresponding elements must be equal.
Comparing the corresponding elements, we get
$\begin{bmatrix}2\text{x} + 1 = \text{x} + 3&5\text{x}=10\\0=0&\text{y}^2+1=26\end{bmatrix}$
On simplifying, we get
x = 2 and $\text{y}=\pm5$
Therefore, x + y = 2 + 5 = 7
or x + y = 2 - 5 = -3
Hence, the value of (x + y) is 7, -3.

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