Finding Symmetric and Skew-Symmetric Matrixes B and C for A=B+C

[ashina14]

Homework Statement

A matrix B is symmetric if B=transpose B.

A matrix C is skew-symmetric if C=−transpose C.

Let A be the matrix given by

A=[[3,6],[-2,1]]

Determine any symmetric matrix B and any skew-symmetric C such that A=B+C

Homework Equations

All given above. Don't know if I need any more.

3. My attempt and issue

I think two equations can be made A =B+C and A = BT - CT
Don't know how to solve them

 

[scurty]

It's been awhile since I've done matrices, but I'll give it a shot. I believe your two equations are correct, you just need to solve for B and C.

Here is what I would do: Solve for either B or C in the first equation ( $A = B + C$ ), plug it into the second equation and use this property: $(A+B)^{T}=A^{T}+B^{T}$. See if that gets you anywhere!

 

[Dick]

A+A^T is symmetric, and A-A^T is antisymmetic, yes? Tell me why? Can you think of some way to combine them to get A?