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.

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- January 31st 2007, 12:31 AMkwtolleyAugmented matrix
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. - January 31st 2007, 04:24 AMAfterShock
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. - January 31st 2007, 06:02 AMSoroban
Hello, kwtolley!

You're into matrices and you still don't know how to check your answers ??

. . Shame! .Go to your room!

Quote:

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: .

- January 31st 2007, 08:39 AMkwtolleyThanks to you both
Thanks again, I see where I messed up.