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

Let n [tex]\geq[/tex]2. Which of the conditions defining a subspace are satisfied for the following subsets of the vector space Mnxn(R) of real (nxn)-matrices? (Proofs or counterexamples required.

There are three subsets, i will start with the one where The subset V is that of square matrices with determinant = 0.

So in this case i know that these matrices aren't invertible but it isnt a criteria of subspaces for there to be a multiplicative inverse. The first axiom is that there is a zero vector 0v such that x of V time 0v = 0. But how would i write a proof for this?

Then the other axioms i need to show are closure under addition and scalar multiplication, an additive identity element (0), and an additive inverse. I dont need to show multiplicative inverse, no? I mean in any case to show the set is a subspace?

Any help is appreciated, thanks

2. Relevant equations

3. The attempt at a solution

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# Subspace criteria applied to square matrices, proof help

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