Construct a 2×2 matrix A=[aij], whose element aij is 2(i+j)2.

⇒ aij=2(i+j)2aiji=,j= aij=2(i+j)2 a11i=1,j=1 a11=2(1+1)2=2(2)2=24=2 a12i=1,j=2 a12=2(1+2)2=2(3)2=29 a21 i=2,j=1 a21=2(2+1)2=2(3)2=29a22 i=2,j=2 a22=2(2+2)2=2(4)2=216=8⇒ Required matrix A=[a11a21a12a22]=⎣⎡229298⎦⎤

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Construct a 2 2 matrix A = [a_{ij}], whose element a_{ij} is

Question

Construct a $2 \times 2$ matrix $A = [a_{ij}]$ , whose element $a_{ij}$ is $\frac{( i + j ) ^{2}}{2}$ .

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Camila Discussed

Construct a

2 \times 2

matrix

A = [a_{ij}]

, whose element

a_{ij}

\frac{( i + j ) ^{2}}{2}

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

\Rightarrow

a_{ij} = \frac{( i + j ) ^{2}}{2}

$a_{ij}$	$i =, j =$	$a_{ij} = \frac{( i + j ) ^{2}}{2}$
$a_{11}$	$i = 1, j = 1$	$a_{11} = \frac{( 1 + 1 ) ^{2}}{2} = \frac{( 2 ) ^{2}}{2} = \frac{4}{2} = 2$
$a_{12}$	$i = 1, j = 2$	$a_{12} = \frac{( 1 + 2 ) ^{2}}{2} = \frac{( 3 ) ^{2}}{2} = \frac{9}{2}$
$a_{21}$	$i = 2, j = 1$	$a_{21} = \frac{( 2 + 1 ) ^{2}}{2} = \frac{( 3 ) ^{2}}{2} = \frac{9}{2}$
$a_{22}$	$i = 2, j = 2$	$a_{22} = \frac{( 2 + 2 ) ^{2}}{2} = \frac{( 4 ) ^{2}}{2} = \frac{16}{2} = 8$

\Rightarrow

Required matrix

A = [a_{11} a_{21} a_{12} a_{22}] = ⎣ ⎡ 2 \frac{9}{2} \frac{9}{2} 8 ⎦ ⎤

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Question Text	Construct a $2 \times 2$ matrix $A = [a_{ij}]$ , whose element $a_{ij}$ is $\frac{( i + j ) ^{2}}{2}$ .
Answer Type	Text solution:1
Upvotes	150

Construct a 2×2 matrix A=[aij​], whose element aij​ is 2(i+j)2​.

Text solutionVerified

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Construct a $2 \times 2$ matrix $A = [a_{ij}]$ , whose element $a_{ij}$ is $\frac{( i + j ) ^{2}}{2}$ .