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Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
Question
Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$a_{ij} = 2i$
✓

Answer

Here, $\text{A}=(\text{a}_\text{ij})_{3\times4}=\begin{bmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}&\text{a}_{14}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}&\text{a}_{24}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}&\text{a}_{34}\end{bmatrix}\ \dots(1)$
$a_{11}=2(1)=2, a_{12}=2(1)=2, a_{13}=2(1)=2, a_{14}=2(1)=2$
$a_{21}=2(2)=4, a_{22}=2(2)=4, a_{23}=2(2)=4, a_{24}=2(2)=4$
$a_{31}=2(3)=6, a_{32}=2(3)=6, a_{33}=2(3)=6 \text { and } a_{34}=2(3)=6$
So, the required matrix is $\begin{bmatrix}2&2&2&2\\4&4&4&4\\6&6&6&6\end{bmatrix}.$

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