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Homework Statement
Determine the null space of the following matrix:
A = [1 1 -1 2
2 2 -3 1
-1 -1 0 -5]
Homework Equations
[itex] Ax=0 [/itex] where [itex] x = (x_{1}, x_{2}, x_{3}, x_{4})^{T}[/itex]
The Attempt at a Solution
If I put the system Ax=0 into augmented form:
1 1 -1 2 | 0
2 2 -3 1 | 0
-1 -1 0 -5 | 0
By row reduction I get the following row echelon form:
1 1 -1 2 | 0
0 0 1 3 | 0
0 0 0 0 | 0
So if
[itex] x = (x_{1}, x_{2}, x_{3}, x_{4})^{T} = (-5t-s, s, -3t, t)^{T}[/itex]
[itex] = t(-5, 0, -3, 1)^{T} + s(-1, 1, 0, 0)^{T}[/itex]
[itex] = Span[ (-5, 0, -3, 1)^{T}, (-1, 1, 0, 0)^{T} ][/itex]
My book has the answer:
[itex] x = (-1, 1, 0, 0)^{T}, Span[ (-5, 0, -3, 1)^{T}][/itex]
Have I gone wrong somewhere or are these answers equivalent? I can't see it if they are...