Construct a 3 × 4 matrix A = [aij] whose element aij are given by… - Vidyadip

Question

Construct a 3 × 4 matrix A = [a_ij] whose element a_ij are given by:
a_ij = 2i

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Answer

Here, $\text{A}=(\text{a}_\text{ij})_{3\times4}=\begin{bmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}&\text{a}_{14}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}&\text{a}_{24}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}&\text{a}_{34}\end{bmatrix}\ \dots(1)$
a₁₁ = 2(1) = 2, a₁₂ = 2(1) = 2, a₁₃ = 2(1) = 2, a₁₄ = 2(1) = 2
a₂₁ = 2(2) = 4, a₂₂ = 2(2) = 4, a₂₃ = 2(2) = 4, a₂₄ = 2(2) = 4
a₃₁ = 2(3) = 6, a₃₂ = 2(3) = 6, a₃₃ = 2(3) = 6 and a₃₄ = 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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