00:01
Okay, so in this question we're given two vectors.
00:04
So vector u, which is 1 -2 -minus 1, vector v, which is minus 2, 3, 4.
00:11
And we want to check that another vector is a linear combination of both, and another one will not be.
00:17
So let's start with the first one.
00:19
So we want to show that w, which is equal to minus 7, minus 7, and 9, can be written as a multiple of some x times the first vector, plus y times the second vectors.
00:33
Let's just write it.
00:35
So we want minus seven to be x times this, so x plus minus 2y.
00:44
We want minus seven to also be 2x plus 3y.
00:50
And we want 9 to be minus x plus 4y.
00:57
So we just have to check that this system is not impossible, there's not a contradiction.
01:02
So first equation gives x as minus 7 plus 2y.
01:07
Replacing on the second equation, we get minus 14 plus 4y plus 3y.
01:14
And replacing on the last equation, we get 7 minus 2y plus 4y.
01:20
Let's make the calculation.
01:22
So first one we leave as it is plus 2y.
01:26
Second equation will give me, i send a 14 to this side, so i will obtain 7 equals 7.
01:33
So i get y equals 1.
01:35
And on the last equation, i get 9 minus 7, 2.
01:38
2 is equal to 2 y...