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## Homework Statement

So I have these two Matrices:

M = \begin{pmatrix}

a & -a-b \\

0 & a \\

\end{pmatrix}

and

N =

\begin{pmatrix}

c & 0 \\

d & -c \\

\end{pmatrix}

Where a,b,c,d ∈ ℝ

Find a base for M, N, M +N and M ∩ N.

## Homework Equations

I know the 8 axioms about the vector spaces.

## The Attempt at a Solution

I chose these fours matrices as a base for the first three vector spaces.

\begin{pmatrix}

1 & 0 \\

0 & 0 \\

\end{pmatrix}

\begin{pmatrix}

0 & 1 \\

0 & 0 \\

\end{pmatrix}

\begin{pmatrix}

0 & 0 \\

1 & 0 \\

\end{pmatrix}

\begin{pmatrix}

0 & 0 \\

0 & 1 \\

\end{pmatrix}

I got that the only vector space satisfying M ∩ N is

\begin{pmatrix}

0 & 0 \\

0 & 0 \\

\end{pmatrix}

If M ∩ N constitutes a vector space, I can use the same base as the other three. But if it doesnt, I have to explain why.

Not sure how to go about that...