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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 = 0, a12 = 1 - 2 = -1, a13 = 1 - 3 = -2, a14 = 1 - 4 = -3
a21 = 2 - 1 = 1, a22 = 2 - 2 = 0, a23 = 2 - 3 = -1, a24 = 2 - 4 = -2
a31 = 3 - 1 = 2, a32 = 3 - 2 = 1, a33 = 3 - 3 = 0 and a34 = 3 - 4 = -1
So, the required matrix is $\begin{bmatrix}0&-1&-2&-3\\1&0&-1&-2\\2&1&0&-1\end{bmatrix}.$

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