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I have this problem, I find it difficult, any hints will be appreciated...

Two subspaces are given (W1 and W2) from the vector space of matrices from order 2x2.

W1 is the subspace of upper triangular matrices

W2 is the subspace spanned by:

\[\left(\begin{matrix}1&0\\1&2\\\end{matrix}\right)\]

\[\left(\begin{matrix}1&1\\2&1\\\end{matrix}\right)\]

\[\left(\begin{matrix}2&1\\0&0\\\end{matrix}\right)\]

a. what is the dimension of the intersection of W1 and W2 ?

b. does:

\[\left(\begin{matrix}6&1\\0&4\\\end{matrix}\right)\]

belong to the intersection ?

thanks !!