# Find a basis for the solution space of the given homogeneous system.

by memo_juentes
Tags: basis, linar algebra, math, spans
 P: 8 1. The problem statement, all variables and given/known data Find a basis for the solution space of the given homogeneous system. x1 x2 x3 x4 1 2 -1 3 | 0 2 2 -1 6 | 0 1 0 0 3 | 0 3. The attempt at a solution When I reduced to reduced row echelon form i get the following matrix: 1 0 0 3 | 0 0 1 0 0 | 0 0 0 1 0 | 0 Which I thought it meant that the basis for the solution space would be: 1 0 0 -3 But apparently it isn't...what am I doing wrong?
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,866 You didn't reduce the matrix correctly. Fix that first.
 P: 8 I'm sorry I actually typed the matrix wrong when making this thread. The correct matrix is: 1 2 -1 3 |0 2 2 -1 6 |0 1 0 3 3 |0
Mentor
P: 21,397
Find a basis for the solution space of the given homogeneous system.

 Quote by memo_juentes When I reduced to reduced row echelon form i get the following matrix: 1 0 0 3 | 0 0 1 0 0 | 0 0 0 1 0 | 0 Which I thought it meant that the basis for the solution space would be: 1 0 0 -3 But apparently it isn't...what am I doing wrong?