0:00
Hello.
00:01
For this question, we are asked to show that the set of all matrices that can be represented in this form, where a, b, and d are just arbitrary real numbers is a subspace of m 2x2, which is the set of all 2 by 2 matrices, which in and of itself is a vector space.
00:22
So we need to check the three subspace criteria.
00:27
So the first subspace criteria is that the zero matrixes, which looks like this is this within h and the answer is yes because i can just set a equal to b equal to d equal to zero and clearly the zero matrix is matrix is within h so i give myself a little check mark here secondly if i add two elements of h do i end up back in h and just a little quick trivial calculation remembering the definition of matrix edition shows me that, yes, this is in fact true.
01:22
And for these types of questions where you're asked to justify that something is, in fact, a subspace, it should be fairly routine, just checking these three criteria.
01:33
And a lot of times, it's just writing down things that seem incredibly obvious.
01:38
And because our field is the real numbers, if i add two real numbers, i end up back in the real numbers.
01:43
So this is in h...