B. For a matrix A with R1 = (2, 1) and R2 = (1, 3), find
the matrix AZ +3A 51
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Answer:
Given, A
1
,A
3
A
2n−1
are skew-symmetric matrices of same order.
⇒A
1
T
=−A
1
,A
3
T
=−A
3
.A
2n−1
T
=−A
2n−1
.(1)
Now, B=∑
r=1
n
(2r−1)(A
2r−1
)
2r−1
⇒B=A
1
+3(A
3
)
3
+5(A
5
)
5
++(2n−1)(A
2n−1
)
2n−1
⇒B
T
=A
1
T
+3(A
3
T
)
3
+.(2n−1)(A
2n−1
T
)
2n−1
⇒B
T
=−A
1
−3(A
3
)
3
−(2n−1)(A
2n−1
)
2n−1
(using (1))
⇒B
T
=−B
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