
GaussJordan Reduction
Solve the following set of homogeneous equations by GaussJordan reduction of the matrix of coefficients (without the column of zeros from the righthand side.
5x+5y5z=0
3x+4y7z=0
2y8z=0
2y3y+6z=0
I know to do GaussJordan reduction for three equations, but not four. How do I do this  I'm pretty confused :(

let's start with the matrix, which is:
[ 5 5 .5]
[ 3 4 7]
[ 0 2 8]
[2 3 6]. since it's easy, multiply the first row by 1/5. then add 2 times the (new) first row to the last row. you should have:
[1 1 .1]
[3 4 7]
[0 2 8]
[0 1 8]. subtract 3 times the first row, from the 2nd, to get:
[1 1 ...1]
[0 1 10]
[0 2 ..8]
[0 1 ..8]. we've effectively eliminated one variable (x) at this point. to continue, let's multiply row 3 by 1/2, and add the new row 3 to row 4:
[1 1 ...1]
[0 1 10]
[0 1 ..4]
[0 0 ...4]. continuing in this way, you should be able to clear out all of column two, except a 1 in row 2. if the 3rd and 4th rows are not 0, continue with column 3, with further rowoperations.