(6.1) Find the values of a, b and c such the matrix below is skew symmetric.
0 0 d
0 2a − 3b + c 3a − 5b + 5c
2 0 5a − 8b + 6c
(6.2) Give an example of a skew symmetric matrix.
(6.3) Prove that A2 is symmetric whenever A is skewsymmetric.
(6.4) Determine an expression for det(A) in terms of det(AT) if A is a square skewsymmetric.
(6.5) Assume that A has an odd number of rows and also an odd number of columns. In this particular case, show that det(·) is an odd function.
1) Given matrix is skew symmetric matrix-
A'=-A
On comparing we get-
On solving above equations we have-
a=0,b=0 and c=0
(2) Skew symmetric matrix is-
(3) Let B=A^2
if
B is symmetric.
Therefore is symmetric.
(4)
(5) Given that A matrix is a square matrix
let n=3 be the order
det() is an odd function
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