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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:
$a_{ij} = j$
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Answer

Here, $\text{A}=(\text{a}_\text{ij})_{3\times4}=\begin{bmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}&\text{a}_{14}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}&\text{a}_{24}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}&\text{a}_{34}\end{bmatrix}\ \dots(1)$
$a_{11} = 1, a_{12} = 2, a_{13} = 3, a_{14} = 4$
$a_{21} = 1, a_{22} = 2, a_{23} = 3, a_{24} = 4$
$a_{31} = 1, a_{32} = 2, a_{33} = 3, a_{34} = 4$
Using Equation (i),
$\text{A}=\begin{bmatrix}1&2&3&4\\1&2&3&4\\1&2&3&4\end{bmatrix}$

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