Construct a 2×2 matrix, A=[aij], whose elements are given by:(i) aij=2(i+j)2(ii) aij=ji(iii) aij=2(i+2j)2

Question

Construct a 2×2 matrix, A=[aij​], whose elements are given by:(i) aij​=2(i+j)2​(ii) aij​=ji​(iii) aij​=2(i+2j)2​

Filo · Accepted Answer

(i) Since it is a 2×2 matrixit has 2 rows and 2 column.Let matrix be AWhere A=[a11​a21​ ​a12​a22​​]Now it is given thataij​=2(i+j)2​ aij​i=,j=  aij​=2(i+j)2​ a11​ i=1,j=1 a11​=2(1+1)2​=2(2)2​=24​=2 a12​ i=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​=29​ a22​ i=2,j=2 a22​=2(2+2)2​=2(4)2​=216​=8Hence,the required matrix A iaA[a11​a21​​a12​a22​​]=⎣⎡​229​​29​8​⎦⎤​(ii) Since it is a 2×2 matrixit has 2 rows and 2 column.Let matrix be AWhere A=[a11​a21​ ​a12​a22​​]Now it is given thataij​=ji​ aij​i=,j=  aij​=ji​ a11​ i=1,j=1 a11​=11​=1 a12​ i=1,j=2 a12​=21​ a21​ i=2,j=1 a21​=12​=2 a22​ i=2,j=2 a22​=22​=1Hence,the required matrix A isA[a11​a21​​a12​a22​​]=[12​21​1​](iii) Since it is a 2×2 matrixit has 2 rows and 2 column.Let matrix be AWhere A=[a11​a21​ ​a12​a22​​]Now it is given thataij​=2(i+2j)2​ aij​i=,j=  aij​=2(i+2j)2​ a11​ i=1,j=1 a11​=2(1+2(1))2​=2(1+2)2​=2(3)2​=29​ a12​ i=1,j=2 a12​=2(1+2(2))2​=2(1+4)2​=2(5)2​=225​ a21​ i=2,j=1 a21​=2(2+2(1))2​=2(2+2)2​=2(4)2​=216​=8 a22​ i=2,j=2 a22​=2(2+2(2))2​=2(2+4)2​=2(6)2​=236​=18Hence,the required matrix A iaA[a11​a21​​a12​a22​​]=[29​8​225​18​]

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

$a_{ij}$	$i =, j =$	$a_{ij} = \frac{i}{j}$
$a_{11}$	$i = 1, j = 1$	$a_{11} = \frac{1}{1} = 1$
$a_{12}$	$i = 1, j = 2$	$a_{12} = \frac{1}{2}$
$a_{21}$	$i = 2, j = 1$	$a_{21} = \frac{2}{1} = 2$
$a_{22}$	$i = 2, j = 2$	$a_{22} = \frac{2}{2} = 1$

$a_{ij}$	$i =, j =$	$a_{ij} = \frac{( i + 2 j ) ^{2}}{2}$
$a_{11}$	$i = 1, j = 1$	$a_{11} = \frac{( 1 + 2 ( 1 ) ) ^{2}}{2} = \frac{( 1 + 2 ) ^{2}}{2} = \frac{( 3 ) ^{2}}{2} = \frac{9}{2}$
$a_{12}$	$i = 1, j = 2$	$a_{12} = \frac{( 1 + 2 ( 2 ) ) ^{2}}{2} = \frac{( 1 + 4 ) ^{2}}{2} = \frac{( 5 ) ^{2}}{2} = \frac{25}{2}$
$a_{21}$	$i = 2, j = 1$	$a_{21} = \frac{( 2 + 2 ( 1 ) ) ^{2}}{2} = \frac{( 2 + 2 ) ^{2}}{2} = \frac{( 4 ) ^{2}}{2} = \frac{16}{2} = 8$
$a_{22}$	$i = 2, j = 2$	$a_{22} = \frac{( 2 + 2 ( 2 ) ) ^{2}}{2} = \frac{( 2 + 4 ) ^{2}}{2} = \frac{( 6 ) ^{2}}{2} = \frac{36}{2} = 18$

Question Text	Construct a $2 \times 2$ matrix, $A = [a_{ij}]$ , whose elements are given by: (i) $a_{ij} = \frac{( i + j ) ^{2}}{2}$ (ii) $a_{ij} = \frac{i}{j}$ (iii) $a_{ij} = \frac{( i + 2 j ) ^{2}}{2}$
Answer Type	Text solution:1
Upvotes	150

Construct a $2 \times 2$ matrix, $A = [a_{ij}]$ , whose elements are given by:
(i) $a_{ij} = \frac{( i + j ) ^{2}}{2}$
(ii) $a_{ij} = \frac{i}{j}$
(iii) $a_{ij} = \frac{( i + 2 j ) ^{2}}{2}$

Text solutionVerified

Practice questions from similar books

Construct a 2×2 matrix, A=[aij​], whose elements are given by:(i) aij​=2(i+j)2​(ii) aij​=ji​(iii) aij​=2(i+2j)2​

Text solutionVerified

Practice questions from similar books

Construct a $2 \times 2$ matrix, $A = [a_{ij}]$ , whose elements are given by:
(i) $a_{ij} = \frac{( i + j ) ^{2}}{2}$
(ii) $a_{ij} = \frac{i}{j}$
(iii) $a_{ij} = \frac{( i + 2 j ) ^{2}}{2}$