Recent content by TrapMuzik

Figured it out! Never mind

Okay, so for the problem before this, I proved that L(S ∩ T ) ⊂ L(S ) ∩ L(T ). For this problem, I have to give an example where L(S ∩ T ) ̸= L(S ) ∩ L(T ). So I'm thinking that there are going to be elements in L(S) intersect L(T) that are not in the span of S intersect T. In what sort...

For this question we are assuming the base axioms. There are later problems where we have to define addition, check closure, etc.

Hi chiro, I may have to go about showing that this space meets all of the axioms, now that you mention it. Thanks for your help!

I should add that there are 3 proofs that I believe build on each other and may be of use for this problem. The first is a proof that 0x= the zero vector Let z=0x z+z= 0x + 0x = (0+0)x (axiom 8) = 0x = z so we have z+z=z, and by axiom 5 we get that z=0 The second proof is for a0=0...

Hey all, So I'm just starting a course in linear algebra, but I don't have much experience with proofs. This problem has been giving me some difficulty. So we have a scalar "a" and vector x. V is a linear space, and x is contained in V. I have to show that if ax=0, where 0 is the zero...