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Matrices — MATHS STD 12 Science — Question

Rajasthan 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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