1. ## Subspaces take 2.

Let $V=\mathbb{R}^4$. Suppose further that $W_1$ is a subsapce of $V$ spanned by vectors $(1,2,0,1)$ and $(1,1,1,0)$, and $W_2$ is a subspace of $V$ spanned by $(2,3,1,1)$.

Determine $dim(W_1+W_2)$ and $dim(W_1 \cap W_2)$.
My other thread might be useful: http://www.mathhelpforum.com/math-he...subspaces.html

Sifting $(1,2,0,1)$ and $(1,1,1,0)$ gives those two vectors. Hence $dim(W_1)=2$.

Similarly $dim(W_2)=1$.

Since $(1,2,0,1)+(1,1,1,0)=(2,3,1,1)$ we know that $W_2$ is a subspace of $W_1$.

Therefore $dim(W_1 \cap W_2)=1$ and $dim(W_1+W_2)=2$.

Is this it? This question was worth 10 marks but my answer is remarkably small!

2. Originally Posted by Showcase_22
My other thread might be useful: http://www.mathhelpforum.com/math-he...subspaces.html

Sifting $(1,2,0,1)$ and $(1,1,1,0)$ gives those two vectors. Hence $dim(W_1)=2$.

Similarly $dim(W_2)=1$.

Since $(1,2,0,1)+(1,1,1,0)=(2,3,1,1)$ we know that $W_2$ is a subspace of $W_1$.

Therefore $dim(W_1 \cap W_2)=1$ and $dim(W_1+W_2)=2$.

Is this it? This question was worth 10 marks but my answer is remarkably small!