construct a 3 × 4 matrix, whose elements are given by: a_ ij =2 i… - Vidyadip

Question

construct a 3 × 4 matrix, whose elements are given by:
$\text a_{\text {ij}}=2{\text{i}}-{\text{j}} $

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Answer

$\text{Let A}=\left[\text a_{\text{ij}}\right]\text {be required}\ 3\times4\ \text{matrix where}\ {\text a_{\text {ij}}} =2{\text{i - j}}$

$\therefore\ \text a_{11}=2-1=1,\ \text a_{12}=2-2=0,$

$ \text a_{13}=2-3=-1,\ \text a_{14}=2-4=-2 $

$\text a_{21}=4-1=3,\ \text{a}_{22}=4-2=2,$

$ \text{a}_{23}=4-3=1,\ \ \text{a}_{24}=4-4=0 $

$\text a_{31}=6-1=5,\ \ \text a_{32}=6-2=4,$

$\text a_{33}=6-3=3,\ \ \text a_{34}=6-4=2 $

$\therefore\ \text A = \begin{bmatrix}1 & 0 &-1 & -2 \\3 & 2&1&0\\\ 5&4&3&2 \end{bmatrix} $

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