00:01
So in this problem, we're given three equations with three unknowns, and we're told we can use any convenient method we want to solve the following system of equations.
00:10
And if the system is dependent, express the solution set in terms of one of the variables.
00:15
And we're going to leave all fractional answers in fraction form.
00:19
So we're given minus 2x plus 6y plus 5z is minus 2.
00:29
X plus 7y minus z equals 28 3x plus y minus 6 z is 30 so we'll build our what i'm going to do is the augmented matrix row reduce it and that will tell us the values for x y and z accordingly so i go to desmos .com to the matrix calculator and i go a new matrix and i have three rows and four columns.
01:19
And i'm beginning in entering the coefficients here.
01:22
First column will be x, second one will be y, third one will be z.
01:26
And the fourth one will be the constants over from the right hand side.
01:30
So i have negative 2, 6, 5, negative 2, and then 1, 7, negative 1, and 28.
02:04
Then i have 3, 1, negative 6, and 30.
02:26
So there's my matrix.
02:27
Now if i do the ref down here, the row reduced echelon form of matrix a, then i get my answer.
02:38
And you notice it's in decimals, and we were told to leave it in fractions.
02:42
So i'll press this right here to put it in fractions.
02:46
And so there is my solution...