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

aij=2∣2i−3j∣ ⇒a11=2∣2×1−3×1∣ =2∣−1∣ =21⇒a12=2∣2×1−3×2∣ =2∣2−6∣ =2∣−4∣ =2⇒a21=2∣2×2−3×1∣ =2∣1∣ =21⇒a22=2∣2×2−3×2∣ =2∣−2∣ =22=1⇒a31=2∣2×3−3×1∣ =2∣3∣ =23⇒a32=2∣2×3−3×2∣ =2∣0∣ =0∴A=⎣⎡21 21 23 210⎦⎤ Hence, solved.

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

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

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Eleanor Discussed

Construct a

3 \times 2

matrix

A = [a_{ij}]

whose elements are given by

a_{ij} = \frac{∣2 i - 3 j ∣}{2}

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

a_{ij} = \frac{∣ 2 i - 3 j ∣}{2}

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

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

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

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

\Rightarrow a_{31} = \frac{∣ 2 \times 3 - 3 \times 1 ∣}{2} = \frac{∣ 3 ∣}{2} = \frac{3}{2}

\Rightarrow a_{32} = \frac{∣ 2 \times 3 - 3 \times 2 ∣}{2} = \frac{∣ 0 ∣}{2} = 0

∴ A = ⎣ ⎡ \frac{1}{2} \frac{1}{2} \frac{3}{2} 210 ⎦ ⎤

Hence, solved.

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

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

Text solutionVerified

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