- #1
stukbv
- 118
- 0
Basically there are 2 equations ;
x+2y+3z = 1 2x+4y+6z=2
I put them into a matrix and row reduce to get
1 2 3 | 1
0 0 0 | 0
so we can say x = 1 - 2y -3z and let y and z = 0 to get a solution is (1,0,0)
Now i need to find the nullspace to find the whole solution set;
so x + 2y + 3z = 0
Ive been told the full answer to the set of solutions is
(1,0,0)+ { a(2,-1,0) + b(-3,0,1) | a,b are in reals}
How do they get those solutions for the nullspace, i can see they have set y = 0 and z=0 to get the 2 vectors but how do you know which ones to set = 0, i.e. why couldn't i set x =0 to get a solution in the nullspace??
Thanks so much!
x+2y+3z = 1 2x+4y+6z=2
I put them into a matrix and row reduce to get
1 2 3 | 1
0 0 0 | 0
so we can say x = 1 - 2y -3z and let y and z = 0 to get a solution is (1,0,0)
Now i need to find the nullspace to find the whole solution set;
so x + 2y + 3z = 0
Ive been told the full answer to the set of solutions is
(1,0,0)+ { a(2,-1,0) + b(-3,0,1) | a,b are in reals}
How do they get those solutions for the nullspace, i can see they have set y = 0 and z=0 to get the 2 vectors but how do you know which ones to set = 0, i.e. why couldn't i set x =0 to get a solution in the nullspace??
Thanks so much!