The following matrix is obtained from a augmented matrix, system of equations.
1 0 3 20
0 1 2 -2
0 0 1 4 my answer is 20,-2,4 is this right, thanks for checking my answer.
You have:
x_1 + 3x_3 = 20
x_2 + 2x_3 = -2
x_3 = 4;
You can check yourself to see if this works.
20 + 4(3) = 24? No.
Get the matrix in row reduced echelon form. First, -2*Row 3 + Row 2
= Matrix([[1, 0, 3, 20],[0, 1, 0, -10],[0, 0, 1, 4]]
-3*Row 3 + Row 1
= Matrix([[1, 0, 0, 8],[0, 1, 0, -10],[0, 0, 1, 4]]
Now:
x_1 = 8
x_2 = -10
x_3 = 4
8 + 3(4) = 20? Yes.
-10 + 2(4) = -2? Yes.
x_3 = 4? Yes.
Hello, kwtolley!
You're into matrices and you still don't know how to check your answers ??
. . Shame! .Go to your room!
The following matrix is obtained from a augmented matrix, system of equations:
. .
Most of it already reduced; we need to clear the third column only.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
The original system of equations is ridiculously simple:
. . . .
. . . . .
. . . . . . . . .
We already have one answer: .
Substitute into the second equation: .
Substitute into the first equation: .