00:01
We're going to use matrices to solve this problem.
00:03
What we have is that a player, coach, and assistant have earned $50 ,000.
00:09
We've also given that the coach is one -half the amount of the player in terms of earnings, and the assistant coach earned one -third the amount of the head coach.
00:21
So the first line that all three made $50 ,000 will give us an equation x plus y plus z equals $50 ,000.
00:32
Let me just say that x is the player amount, y is the coach, and z is the assistant.
00:55
And then the next line of our problem, we're going to have that the coach, which is y, is equal to a half of x, the player.
01:09
And then the next line would be that the assistant z is one -third the coach, which is represented by y again.
01:19
And then these two equations that i made, i'm going to rewrite those as negative a half x plus y equals zero, and then negative one -third y plus z equals zero.
01:37
I do this to be able to write it in matrix form, where column one, column two, column three are x, y, and z.
01:46
So my first line here is going to be one, one, one, and $50 ,000.
01:53
Next line would be negative one -half, one, zero, and zero.
02:00
Then the next line is zero, negative one -third, one, and zero.
02:05
I'm going to do this by eliminating the fractions, one -half and one -third.
02:12
So i'm going to take two times row two to get a new row two, three times row three to get a new row three.
02:22
All right, so the resulting matrix will have the first line be the same.
02:28
The second line will be negative one, two, zero, and zero.
02:34
And then the last line will be zero, negative one, three, and zero.
02:40
So then what i'll do is i'm going to cancel out the negative one right here...