- #1
caljuice
- 70
- 0
So an example was the matrix:[tex]
A = \left(\begin{array}{cccc}
a&a+b\\
b&0\\
\end{array}
\right)
[/tex] is a subspace of M2x2.
and is the linear combination [tex]
a*\left(\begin{array}{cccc}
1&1\\
0&0
\end{array}
\right)
[/tex] + [tex]
b*\left(\begin{array}{cccc}
0&1\\
1&0
\end{array}
\right)
[/tex]
Meaning it has dimension 2. But I'm not sure how it comes to this conclusion.
Dimension means # of vectors in a basis. However, I don't know how to translate this matrix addition in terms of vectors. Is the dimension 2 because there are 2 matrices being added? Or because we can break it down into the linear combination of indepedent vectors v1 =(1,0) v2=(0,1)? Or is it completely something else? thanks.
A = \left(\begin{array}{cccc}
a&a+b\\
b&0\\
\end{array}
\right)
[/tex] is a subspace of M2x2.
and is the linear combination [tex]
a*\left(\begin{array}{cccc}
1&1\\
0&0
\end{array}
\right)
[/tex] + [tex]
b*\left(\begin{array}{cccc}
0&1\\
1&0
\end{array}
\right)
[/tex]
Meaning it has dimension 2. But I'm not sure how it comes to this conclusion.
Dimension means # of vectors in a basis. However, I don't know how to translate this matrix addition in terms of vectors. Is the dimension 2 because there are 2 matrices being added? Or because we can break it down into the linear combination of indepedent vectors v1 =(1,0) v2=(0,1)? Or is it completely something else? thanks.