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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
Construct a 3 $\times$ 4 matrix, whose elements are given by $a_{ij} = 2i - j$
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Answer

In general $3 \times 4$ matrix is given by $A = \left[\begin{array}{llll} {a_{11}} & {a_{12}} & {a_{13}} & {a_{14}} \\ {a_{21}} & {a_{22}} & {a_{23}} & {a_{24}} \\ {a_{31}} & {a_{32}} & {a_{33}} & {a_{34}} \end{array}\right]$
$a_{ij} = 2i - j, i = 1, 2, 3$ and $j = 1, 2, 3, 4$
Therefore,
$  a_{11}=2 \times 1-1=2-1=1 $
$  a_{21}=2 \times 2-1=4-1=3 $
$  a_{31}=2 \times 3-1=6-1=5 $
$  a_{12}=2 \times 1-2=2-2=0  $
$ a_{22}=2 \times 2-2=4-2=2  $
$  a_{32}=2 \times 3-2=6-2=4 $
$  a_{13}=2 \times 1-3=2-3=-1 $
$  a_{23}=2 \times 2-3=4-3=1  $
$  a_{33}=2 \times 3-3=6-3=3 $
$  a_{14}=2 \times 1-4=2-4=-2  $
$  a_{24}=2 \times 2-4=4-4=0  $
$ a_{34}=2 \times 3-4=6-4=2$ 
Therefore, required matrix is $A = \left[\begin{array}{cccc} {1} & {0} & {-1} & {-2} \\ {3} & {2} & {1} & {0} \\ {5} & {4} & {3} & {2} \end{array}\right]$

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