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

Let k be a field, V = Mat2x2(k), U:={[a, b], [-b, a] a, b E k} and W:={[a, b], [b, -a] a, b E k}. Show that V is the direct sum of U and W.

2. Relevant equations

3. The attempt at a solution

Add the matrix for U to the matrix of W. Values in that matrix still exist in k, so V = U + W. Is that the right reasoning? How do you show the intersection of two matrices is 0? Very confused.

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# How to show the direct sum of two matrices?

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