construct a matrix of 2*2 order whose elements aij are given by aij=(-1)i+j
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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
ij
=
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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