Dimension of the linear span of a vector

[lolimcool]

Homework Statement

find the dimension of the linear span of the given vectors
v1 = ( 2, -3, 1) v2 = ( 5, -8, 3) v3 = (-5, 9, -4)

Homework Equations

The Attempt at a Solution

so all i did was make it a matrix and put it in rref and i got
[1 0 0]
[0 1 0]
[0 0 1]

does this mean dimensions of the linear span = 3?

 

[HallsofIvy]

Yes, it does. What you have shown is that those three vectors are independent and independent vectors form a basis for their span.

 

[Dick]

Yes, it does. What you have shown is that those three vectors are independent and independent vectors form a basis for their span.

It would mean that. Except I think you did the row reduction wrong. Those vectors aren't linearly independent.

 

[lolimcool]

It would mean that. Except I think you did the row reduction wrong. Those vectors aren't linearly independent.

oops i did i did it again and got

1 0 5
0 1 -3
0 0 0

so dimension = 2?

 

[Dick]

oops i did i did it again and got

1 0 5
0 1 -3
0 0 0

so dimension = 2?

Yes, dimension=2.