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Construct a2 x2 matrix A= [a;;| whose elements are given by[aj; =[ (i)2 —j ] |
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Answer» Answer: Since it is a 2×2 matrix it has 2 rows and 2 column. Let matrix be A Where A=[ a 11
a 21
a 12
a 22
] Now it is given that a
= 2 (i+j) 2
a ij
i=,j= a ij
= 2 (i+j) 2
a 11
i=1,j=1 a 11
= 2 (1+1) 2
= 2 (2) 2
= 2 4
=2 a 12
i=1,j=2 a 12
= 2 (1+2) 2
= 2 (3) 2
= 2 9
a 21
i=2,j=1 a 21
= 2 (2+1) 2
= 2 (3) 2
= 2 9
a 22
i=2,j=2 a 22
= 2 (2+2) 2
= 2 (4) 2
= 2 16
=8 Hence, the required matrix A ia A[ a 11
a 21
a 12
a 22
]= ⎣ ⎢ ⎢ ⎡
2 2 9
2 9
8
⎦ ⎥ ⎥ ⎤
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