(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let V = M2(R) be the vector space over R of 2×2 real matrices. We consider the mapping

F : V −> V defined for all matrix M belonging to V , by F(M) = AM +MA^T where A^T denotes the transpose matrix of the matrix A given below

A =

1 2

−1 0

Question is: Determine a basis of Ker(F)

3. The attempt at a solution

So I showed that F is a linear operator, and preserves scalar addition and multiplication.

However I am lost as to how I can solve the equation:

AM +MA^T = 0

Any help appreciated, thanks :)

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# Homework Help: Basis of Kernel (matrices)

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