Question

@ganeshie8

Answer 1

my reasoning, it is possible W contains the zero, since so it contains the 0 element, then let B and C be 5x2 matrices in the subspace W, we get FB+FC = 0 closure under addition and then for scalar multiplication let g i guess be a constant (an element of W) we get F(gA)=g(FA)=0 then W is a subspace of all 5x2 matrices

Answer 2

I think this is mostly correct, but has some technical issues. I'll just slightly tweak what you're saying, but overall what you're saying is good.

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so it contains the 0 element,
\[F0=0\]

then let B and C be 5x2 matrices in the subspace W, then their sum A=B+C is also in the subspace.
\[FA=F(B+C)=FB+FC=0+0 =0 \]The main point is: \[FA=0\]

W is a space of matrices, so there are no scalars in it exactly, but your proof is good.

To end, W is a subspace of all 5x2 matrices _that satisfy FA=0_. Not all matrices that we can multiply F by are in this subspace (which has a special name actually, it's called the null space)

Answer 3

Hey I actually had exactly that, I was being lazy and didn't write it all out haha

Answer 4

Good stuff man, I'm sort of liking this stuff, I had no idea what I was doing at the start of the day and now I'm like subspace, basis and all that good stuff xd

Answer 5

rofl niiiiice