I am having a bit of difficulty finding an example that works for this question. It asks to find subspaces W1, W2, and K, in vector space V such that
V = K *direct sum* W1
V = K *direct sum* W2
but W1 does not equal W2.
I have considered using K as R^n, and W1 as 0, and W2, as one vector in R^n. however, K and W2 have a non-zero intersection. Am I thinking in the wrong vector space?