- #1
Alex Langevub
- 4
- 0
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...