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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Construct a $2 × 2$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are given by:
$\text{a}_\text{ij}=\frac{(\text{i}-2\text{j})^2}{2}$
✓

Answer

Here,
$\text{a}_{11}=\frac{[1-2(1)]^2}{2}=\frac{(1-2)^2}{2}=\frac{(-1)^2}{2}=\frac{1}{2},$ $\text{a}_{12}=\frac{[1-2(2)]^2}{2}=\frac{(1-4)^2}{2}=\frac{(-3)^2}{2}=\frac{9}{2}$
$\text{a}_{21}=\frac{[2-2(1)]^2}{2}=\frac{(2-2)^2}{2}=\frac{0}{2}=0,$ $\text{a}_{22}=\frac{[2-2(2)]^2}{2}=\frac{(2-4)^2}{2}=\frac{(-2)^2}{2}=\frac{4}{2}=2$
So, the required matrix is $\begin{bmatrix}\frac{1}{2}&\frac{9}{2}\\0&2\end{bmatrix}.$

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