So an example was the matrix:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

A = \left(\begin{array}{cccc}

a&a+b\\

b&0\\

\end{array}

\right)

[/tex] is a subspace of M_{2x2}.

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 v_{1 }=(1,0) v_{2}=(0,1)? Or is it completely something else? thanks.

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# Subspace matrix, dimension and basis

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