00:01
In this problem, we want to draw vectors u and v and see how we can write vector w as a linear combination of u and v.
00:10
So let's start by drawing our two vectors.
00:20
So u is equal to the vector minus 2, 3.
00:24
So starting at the origin, u points minus 2 units along the x -axis and 3 units along the positive y -axis, like so.
00:37
So vector v is equal to the vector 2, 1.
00:50
So pointing 2 units in the positive x -axis and 1 unit in the positive y -axis.
01:04
And vector w, 2, 9, points 2 units in the positive x -axis and 9 units in the positive y -axis.
01:28
So now i want to see how we can use this to write vector w as a linear combination of u and v.
01:37
So if we were to extend v twice and then add u to this, we appear to have w.
01:57
Indeed, u plus 2 times v is equal to minus 2, 3 plus 4, 1 equal to the vector 2, 4...