00:01
Okay, so the problem, the first one asks you to find these bases for the subspace, which is given by 2y plus, i think this should be a 5, z equals 0.
00:19
Then let's write this in terms of one of the variables.
00:24
So we'll write this as z is equal to 3 over 5 minus 3 over 5x minus 2 over 5y.
00:36
So the subspace is given by all functions, all vectors of the form x, y, minus 3 over 5x minus 2 over 5y.
00:51
Y.
00:52
Now to find the basis, let's split it up into the different components.
00:59
So we can write this as x times 1, 0, minus 3 over 5, plus y times 0, 1, minus 2 over 5.
01:17
So the basis are just these two two vectors.
01:20
So this is the basis.
01:25
And since there's two vectors in the basis, the dimension is equal to two.
01:38
Okay.
01:41
For the second one, it's a bit unclear because x, y is not a, is not a plane.
01:47
So maybe, so i'm going to assume it says x plus y equals zero.
01:51
And i assume this in r3? well, ah, maybe it is x times y.
02:02
Okay, so we'll write this as x times y is equal to 0 if you assume it's in r3.
02:08
So what does this mean? this means either y is equal to 0 or x is equal to 0, right? so you have vectors.
02:21
So the vectors that this can be a part of is either you have some x, 0, and then some z, or you have vectors of the form 0, y, and some c.
02:45
Right? okay, so what is the basis for this? well this means that as a basis, well, you can either write it as x times 1, 0, 0...