How would I solve the following set of equations using matrices (row operations)?

[sktsasus]

[h=1]6x-4y+5z=-37[/h][h=1]5x+4y+4z=-30[/h][h=1]-3x+3y+2z=-4[/h]
My main problem is getting the matrix into row-echelon form.

 

[tkhunny]

First, it would seem reasonable to put it in a matrix form. Let's see your work.

 

[sktsasus]

6 -4 5 -37 I know there should be a line between the third and final column.
5 4 4 -30
-3 3 2 -4

I got to this part but then I got stuck.

 

[mmm4444bot]

6 -4 5 (line here) -37
5 4 4 -30
-3 3 2 -4

I got to this part but then I got stuck.

You don't need to show the vertical line because we already saw the equations (that is, we know it's an augmented coefficient matrix).

For aligning the matrix columns, enclose the text in [code] and [/code] tags. Also, choose a fixed-width font, like Courier New.

[FONT=courier new]
 6  -4   5  -37
 5   4  -4  -30
-3   3   2   -4

[/FONT]

You want the element in R1C1 (row1 column1) to be 1, instead of 6. There's a 5 right below it, so replace R1 with R1 minus R2:

R1 - R2 ==> R1

After that, use the 1 in R1C1 to zero out the elements in R2C1 and R3C1. In other words:

R2 - 5*R1 ==> R2

R3 + 3*R1 ==> R3

Show us what you get. :cool:

 

[stapel]

6 -4 5 -37 I know there should be a line between the third and final column.
5 4 4 -30
-3 3 2 -4

I got to this part but then I got stuck.

Have you studied "row operations" yet?