How to show that $R^3$ is the direct sum of $W_1=$Span$(1,1,1)$ and $W_2=$Span$(\{1,0,0\}, \{1,1,0\})$?
So we write it as $R^3=W_1+W_2$ because every $(x_1, x_2, x_3)\in R^3$ can be written as $a((1,1,1)-(1,1,0))+b((1,1,0)-(1,0,0))+c(1,0,0)$
Do I have the correct direction?