Question

Show that U={u1, u2, u3}, where u1=(1,1,0), and u2=(0,1,0), u3=(-1,0,1) is a basis for R3.

Answer 1

all you need to do is show that this is row equivalent to the identity matrix

Answer 2

i.e. show that these three vectors are linearly independent

Answer 3

You could also set up a 3x3 matrix and take the determinant. If it is non-zero then the set is linearly independent, and 3 linearly independent vectors form a basis for R3.

Answer 4

if i wanted to put it in an augmented matrix would i put in the zero vector as well and then reduce, or just reduce the matrix with the 3 vectors.

Answer 5

just reduce the matrix with the 3 vectors

Answer 6

and if there are 3 pivots then it is independent right

Answer 7

all those theorems about uniqueness and linear independence are related

Answer 8

yes, or if the determinant is zero, or like ten other ways to check
hold on let me find the list of all the things that are equivalent...

Answer 9

sweet, thanks... that would be awesome

Answer 10

Theorem 8 on here shows how all these theorems are connected
http://tutorial.math.lamar.edu/Classes/LinAlg/FundamentalSubspaces.aspx
proving any one of these proves all the others

Answer 11

okay, that you. i appreciate your help again.

Answer 12

I suggest you go with (c) (getting the 3 pivots as you call it) or (g) showing the determinant is non-zero

welcome!

Answer 13

anytime