Construct a 2×3 matrix A=[aij] whose elements are given by aij=21∣2i−3j∣

We have [a11a21 a12a22a13a23]Since aij=21∣2i−3j∣a11=21∣2×1−3×1∣=21∣2−3∣=21∣−1∣=21a12=21∣2×1−3×2∣=21∣2−6∣=21∣−4∣=24=2a13=21∣2×1−3×3∣=21∣2−9∣=21∣−7∣=27a21=21∣2×2−3×1∣=21∣4−3∣=21∣1∣=21a22=21∣2×2−3×2∣=21∣4−6∣=21∣−2∣=22=1a23=21∣2×2−3×3∣=21∣4−9∣=21∣−5∣=25Hence the required matrix is A=⎣⎡2121 212725⎦⎤

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Construct a 2 3 matrix A=[{a}_{ij}] whose elements are given b

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Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = \frac{1}{2} ∣ 2 i - 3 j ∣$

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Construct a

2 \times 3

matrix

A = [a_{ij}]

whose elements are given by

a_{ij} = \frac{1}{2} ∣ 2 i - 3 j ∣

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Text solutionVerified

We have

[a_{11} a_{21} a_{12} a_{22} a_{13} a_{23}]

Since

a_{ij} = \frac{1}{2} ∣ 2 i - 3 j ∣

a_{11} = \frac{1}{2} ∣ 2 \times 1 - 3 \times 1 ∣ = \frac{1}{2} ∣ 2 - 3 ∣ = \frac{1}{2} ∣ - 1 ∣ = \frac{1}{2}

a_{12} = \frac{1}{2} ∣ 2 \times 1 - 3 \times 2 ∣ = \frac{1}{2} ∣ 2 - 6 ∣ = \frac{1}{2} ∣ - 4 ∣ = \frac{4}{2} = 2

a_{13} = \frac{1}{2} ∣ 2 \times 1 - 3 \times 3 ∣ = \frac{1}{2} ∣ 2 - 9 ∣ = \frac{1}{2} ∣ - 7 ∣ = \frac{7}{2}

a_{21} = \frac{1}{2} ∣ 2 \times 2 - 3 \times 1 ∣ = \frac{1}{2} ∣ 4 - 3 ∣ = \frac{1}{2} ∣ 1 ∣ = \frac{1}{2}

a_{22} = \frac{1}{2} ∣ 2 \times 2 - 3 \times 2 ∣ = \frac{1}{2} ∣ 4 - 6 ∣ = \frac{1}{2} ∣ - 2 ∣ = \frac{2}{2} = 1

a_{23} = \frac{1}{2} ∣ 2 \times 2 - 3 \times 3 ∣ = \frac{1}{2} ∣ 4 - 9 ∣ = \frac{1}{2} ∣ - 5 ∣ = \frac{5}{2}

Hence the required matrix is

A = ⎣ ⎡ \frac{1}{2} \frac{1}{2} 21 \frac{7}{2} \frac{5}{2} ⎦ ⎤

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Question Text	Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = \frac{1}{2} ∣ 2 i - 3 j ∣$
Answer Type	Text solution:1
Upvotes	150

Construct a 2×3 matrix A=[aij​] whose elements are given by aij​=21​∣2i−3j∣

Text solutionVerified

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Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements are given by $a_{ij} = \frac{1}{2} ∣ 2 i - 3 j ∣$