Question

Solve by using the Gauss-Jordan elimination method:
x+y-z=2
2x+3y-z=7
3x-2y+z=9
I know that you have to convert them to
1 0 0 | 2
0 1 0 | 7
0 0 1 | 9
I am just not clear on how to do this row by row.
Any help would be greatly appreciated.

Answer 1

Start with the given matrix: {{{(matrix(3,4,1,1,-1,2,2,3,-1,7,3,-2,1,9))}}} Add -2*Row 1 to Row 2 to get the new Row 2 {{{(matrix(3,4,1,1,-1,2,0,1,1,3,3,-2,1,9))}}} Add -3*Row 1 to Row 3 to get the new Row 3 {{{(matrix(3,4,1,1,-1,2,0,1,1,3,0,-5,4,3))}}} Add 5*Row 2 to Row 3 to get the new Row 3 {{{(matrix(3,4,1,1,-1,2,0,1,1,3,0,0,9,18))}}} Multiply Row 3 by {{{1/9}}} to make the pivot 1: {{{(matrix(3,4,1,1,-1,2,0,1,1,3,0,0,1,2))}}} Add -1*Row 3 to Row 2 to get the new Row 2 {{{(matrix(3,4,1,1,0,4,0,1,0,1,0,0,1,2))}}} Add -1*Row 2 to Row 1 to get the new Row {{{(matrix(3,4,1,0,0,3,0,1,0,1,0,0,1,2))}}} The matrix is now in <font size=4><b>reduced row echelon form</b></font> If you need more help with row reduction or Gaussian elimination, check out <a href=http://www.math.odu.edu/~bogacki/lat/> The Linear Algebra Toolkit</a>, and it will take you step-by-step through any Gaussian elimination problem.