Do these linear spaces intersect transversally? (For a,b, find a relationship between $n,l$ and $k$ that do so.
a. $\mathbb{R^k}\times \{0\}$ and $\{0\}\times \mathbb{R^l} $ in $\mathbb{R^n}$
b. $\mathbb{R^k}\times \{0\}$ and $\mathbb{R^l}\times \{0\}$ in $\mathbb{R^n}$
c. $V\times \{0\}$ and diagonal in $V\times V$
My Try:
What I know is two subspaces $V,W$ in $\mathbb{R^n}$ intersect tranversally means $V+W=\mathbb{R^n}$. So for part a, is $n=k+l$ would do that? But I have no idea about part b,c. Please help.