00:01
Okay, so in part a here, we want to find 2u.
00:03
So that's going to be equal to 2 times our vector u, which is negative 2, comma, negative 1.
00:11
So we multiply each component by 2, multiply by a scalar, right? so we just, we have 2 times negative 2 is negative 4, and 2 times negative 1 is negative 2.
00:21
So therefore we have that 2u is equal to the vector negative 4, comma, negative 2.
00:27
Okay, now in part b, we want to find 2u plus 3v.
00:35
So 2u plus 3v.
00:38
We found 2u already, right? that's the vector negative 4, negative 2.
00:42
So we have negative 4, negative 2, but then plus 3v.
00:47
What is 3v? that's 3 times the vector negative 22, right? 3v is equal to 3 times the vector.
00:57
Negative 3, 2, which gives us 3 times negative 3, which is negative 9, and then 3 times 2, which is 6.
01:07
So we're adding here, negative 4, negative 2 plus the vector negative 2, 6.
01:11
We just then add corresponding components.
01:15
So we have negative 4 plus negative 9, which is negative 4 minus 9, which is negative 13 for our first component.
01:24
And then we have negative 2 plus 6, which is 4.
01:28
So therefore we have that 2u plus 3v is equal to the vector negative 13, comma, 4...