Express the matrix A={:[(4,2,-1),(3,5,7)...

Express the matrix `A={:[(4,2,-1),(3,5,7),(1,-2,1)]:}` as the sum of a symmetric matrix and a skew-symmetric matrix.

Verified by Experts

The correct Answer is:

`A={:[(4,5/2,0),(5/2,5,5/2),(0,5/2,1)]:} + {:[(0,-1/2,-1),(1/2,0,9/2),(1,-9/2,0)]`

Similar Questions

Explore conceptually related problems

Express the marix A=|{:(3,2,3),(4,5,3),(2,4,5):}| as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix A=[{:(-3,4,1),(2,3,0),(1,4,5):}] as the sum of symmetric matrix and a skew-symmetric matrix.

(b) answer the foll. Questions: (i) express the matrix A=[[3,2,3],[4,5,3],[2,4,5]] as the sum of a symmetric matrix and a skew -symmetric matrix.

Express the matrix B=[(2,-2,-4),(-1,3,4),(1,-2,-3)] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A={:[(-3,4,1),(2,3,0),(1,4,5)] as the sum of a symmetric and a skew. Symmetric matrix.

Express [[4,3,7],[6,5,-8],[1,2,6]] as the sum of a symmetric matrix and a skew symmetric matrix .

Express the matric A= [[-3,4,1],[2,3,0],[1,4,5]] as the sum of a symmetric matrix and a skex symmetric matrix.

If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C , where B is symmetric matrix and C is skew-symmetric matrix, then find matrices B and C.

If the matrix A is both symmetric and skew symmetric then

If A is symmetric as well as skew-symmetric matrix, then A is