(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The set of all 2x2 singular matrices is not a vector space. why?

[tex]\begin{bmatrix} 1 & 0\\ 0&0 \end{bmatrix}+\begin{bmatrix} 0 & 1\\ 0& 1 \end{bmatrix}=\begin{bmatrix} 1 & 1\\ 0 & 1 \end{bmatrix}[/tex]

2. Relevant equations

Is it because the determinant in both are zero, but by performing addition you get a nonsingular matrix from a two singular matrices.

3. The attempt at a solution

det(0)+det(0)=0

c*det(0) = 0

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# (Linear Algebra) Vector Space

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