Q. 10 C4.5( 20 Votes )

# Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

Answer :

As per Theorem 2 “Any square matrix can be expressed as the sum of a symmetric and skew symmetric matrix.” So in order to prove this we will be using Theorem 1 which states that “For any square matrix A with real number entries, A + A’ is a symmetric matrix and A – A’ is a skew symmetric matrix.”

Now, on adding A and A’ we will get,

Now, on subtracting A’ from A we will get,

.

w, Add M and N, we get,

Thus, A is represented as the sum of a symmetric matrix M and a skew symmetric matrix N.

Rate this question :

Which of the following statements are True or False

Transpose of a column matrix is a column matrix.

Mathematics - ExemplarWhich of the following statements are True or False

Transpose of a column matrix is a column matrix.

Mathematics - ExemplarGiven and . Is (AB)’ = B’A’?

Mathematics - ExemplarWhich of the following statements are True or False

If A and B are any two matrices of the same order, then (AB)’ = A’B’.

Mathematics - ExemplarWhich of the following statements are True or False

If then AB and BA are defined and equal.

Mathematics - ExemplarFor the following matrices A and B, verify that (AB)’ = B’A’.

Mathematics - Board Papers

Which of the following statements are True or False

If A and B are any two matrices of the same order, then (AB)’ = A’B’.

Mathematics - ExemplarUse the product to solve the system of equations

Mathematics - Board Papers