Define the sum U $+$ W of two subspaces U and W of a vector space V $,$ and state the circumstances under which this is a direct sum $($written U $$ W $).$ Prove that ifV $=$U$$W andV isfinite$-$dimensional,thendim$($V$)=$dimU$+$dimW.

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The sum of two subspaces U and W of a vector space V is defined as the set U W u w u U w W In othe... View the full answer