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(ii)
(iii)
Solution :
(i) Let A =
(iii)
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
then find (A + 2B)’.
Solution :
(ii)
Solution :
then verify that A’A = I.
(ii) If A =
then verify that A’A = I.
Solution :
Question
7. (i) Show that the matrix A =
is a symmetric matrix.
(ii) Show that the matrix A =
is a skew symmetric matrix.
Solution :
(i) Given: A =
verify that:
(i) (A + A’) is a symmetric matrix.
(ii) (A – A’) is a skew symmetric matrix.
Solution :
Question
9. Find 1/2 (A + A’) and 1/2(A – A’) when A =
Solution :
Question
10. Express the following matrices as the sum of a symmetric and skew symmetric matrix:
(i)
(ii)
(iii)
(iv)
Solution :
.png)
(iii)
(iv)
Therefore, option (B) is correct.
