00:01
So in this problem, the doctors ordered us to take 40 milligrams of vitamin c and 30 milligrams of vitamin d.
00:08
And we've got three supplements that we can do this with.
00:12
The first supplement x has 20 % vitamin c and 30 % vitamin d.
00:18
Y has 40 % c and 20 % d, and z is 30 % c and 50 % d.
00:26
We're asked to make a table to show what the dosages of these three would be.
00:31
So let's write the equations that this represents.
00:35
What we can write is that 20 % of x, so that's 20 over 100 times x, i guess 20%, plus 40 over 100 y, plus 30 over 100 z.
00:55
Well, when i add all those up, those have to equal my 40 milligrams of vitamin c.
01:00
Okay.
01:03
Do the same thing.
01:05
This was vitamin c.
01:07
Let's do the same thing for vitamin d.
01:11
30 over 100x plus 20 over 100 y plus 50 over 100 z is 30 milligrams.
01:29
Okay.
01:30
So this gives me two equations with three unknowns that i could set up in a matrix and solve, couldn't i? so let's multiply everything by 10, first of all, because that zero cancels, that one cancels, that one cancels.
01:45
Same thing happens down here, right? so i can multiply both equations by 10.
01:52
So i have 2x plus 4y plus 3z is equal to 400, and 3x plus 2y plus 2y plus 5 z is equal to 400, and 3x plus 2y plus 5 z is equal to 300.
02:09
So let's write the augmented matrix for this now.
02:11
2, 4, 3, 300, 3, 2, 5, 300.
02:22
Alright, i want to get a 1 in this first entry right here, don't i? so let's take and do row 2 minus row 1 and put it in the first row.
02:41
So i go 3 minus 2, that's a 1.
02:46
2 minus 4, that's a negative 2.
02:49
5 minus 3 is a 2.
02:51
300 minus 400, that's minus 100.
02:56
Okay? 3, 2, 5, 300.
03:03
Now, i want to get a 0 here.
03:08
So i'm going to do row 2 minus 3 times row 1...