The discussion revolves around finding the null space of a given matrix. The matrix in question is a 3x5 matrix, and participants are exploring the implications of its reduced row echelon form (rref) in relation to the null space.
Some participants have provided guidance on understanding the null space and its relationship to the original system of equations. There is an ongoing exploration of how to express the null space in terms of linear combinations of independent vectors.
There is mention of an extra column in the rref that may not be necessary, and participants are working under the constraints of the homework problem, which requires a clear understanding of the null space concept.
Your work so far is OK, but you just need to take it a little further.kkingkong said:Homework Statement
What is the null space of this matrices.
|1 1 0 3 1|
|0 1 -1 0 1|
|1 1 3 0 1|
The Attempt at a Solution
I reduced it to rref using agumented matrice(each one equals to zero )
|1 0 0 4 0 0|
|0 1 0 -1 1 0|
|0 0 1 -1 0 0|
and i get get x1=-x4 , x2= x4 + -x5, x3 = x4
but then what is the null space??
x[SUB]1[/SUB] = -x[SUB]4[/SUB]
x[SUB]2[/SUB] = x[SUB]4[/SUB] - x[SUB]5[/SUB]
x[SUB]3[/SUB] = x[SUB]4[/SUB]
x[SUB]4[/SUB] = x[SUB]4[/SUB]
x[SUB]5[/SUB] = x[SUB]5[/SUB]Slight correction: the nullspace is the set of all vectors that your matrix would map to the zero vector.Rellek said:Remember that the nullspace is the set of all vectors that would send your original system to the zero vector.
Rellek said:If you could find a set of vectors that are independent and send your system to the zero vector, then it seems as though the span of those vectors would be your entire nullspace.
I think you can get it from there!