00:01
Okay, so we have four vectors v1, v2, v3, v4 in r4, and we're told that v3 is not a linear combination of v1, v2 and v4.
00:13
And then the question is, must it be the case that this set v1, v2, v3, v4, is linearly independent? okay, so is this true or false? and this is going to be, in general, false.
00:26
So it could be the case, but the problem is not always the case, and we can just quickly give a counter -example.
00:32
So when you have questions like this, the best idea is trying to find the simplest counter -example that you can.
00:39
So we want v -3 to not be a linear combination of v -1, v -2 and v -4.
00:43
So why don't we take v -1 to be 1 -0 -0 -0? v -2 to be 2 -0 -0 -0 -0.
00:54
V -3 to be, let's say, 0 -1 -0...