- #1

looper

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## Homework Statement

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.

## Homework Equations

## 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.