Answer:
(i)
Let
and
Let
is a
symmetric matrix.
Also,
let
.
is a skey
symmetric matrix.
Now
Thus
A is represented as the sum a symmetric and a skey symmetric matrix.
(ii) Let
Let
is a
symmetric matrix.
Also, let
is a skew
symmetric matrix.
Now
Thus
A is represented as the sum of a symmetric and a skew symmetric matrix.
(iii)
Let
and
Let
is a symmetry
matrix.
Also,
let
is a skew
symmetric matrix.
Now
P + Q =
Thus
A is represented as the sum of a symmetric and a skew symmetric matrix.
(iii) Let
and
Let
is a
symmetric matrix.
Also, let
is a skew
symmetric matrix.
Now
Thus
A is represented as a sum of symmetric and a skew symmetric matrix.
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