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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
Question
Construct a 3 × 4 matrix A = [aij] whose element aij are given by:
aij = i + j
✓

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 = 1 + 1 = 2, a12 = 1 + 2 = 3, a13 = 1 + 3 = 4, a14 = 1 + 4 = 5
a21 = 2 + 1 = 3, a22 = 2 + 2 = 4, a23 = 2 + 3 = 5, a24 = 2 + 4 = 6
a31 = 3 + 1 = 4, a32 = 3 + 2 = 5, a33 = 3 + 3 = 6, a34 = 3 + 4 = 7
Using equation (i)
$\text{A}=\begin{bmatrix}2&3&4&5\\3&4&5&6\\4&5&6&7\end{bmatrix}$

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