00:01
So if we're told that you and v are in the span of these three vectors, well, essentially, that just means is this here by definition.
00:11
We can take some linear combination, so with just some constants, a1, a2, a3, and say, b1, b2, b3, multiply these with each of those vectors, add them together, and for some numbers, we should get u and v out.
00:26
So if we want to show that this is in the span, all we need to do is show that we should, we can write this as some linear combination.
00:34
So let's just actually just add what we have over here.
00:37
So this would be the vector u plus the vector v, and then notice we can factor out that w1, w2, and w3, which would give us a1 plus b1 times the vector w1 plus a2, times the vector w2, and then plus a3 plus a3 plus b3 times the vector w2...