SOLUTION: I have no idea what this question is asking: Let B={v1, v2, v3} be a set of linearly independent vectors in R^3. Provev that B is a basis for R^3.

Algebra ->  College  -> Linear Algebra -> SOLUTION: I have no idea what this question is asking: Let B={v1, v2, v3} be a set of linearly independent vectors in R^3. Provev that B is a basis for R^3.      Log On


   

Question 31478: I have no idea what this question is asking:
Let B={v1, v2, v3} be a set of linearly independent vectors in R^3. Provev that B is a basis for R^3.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
I have no idea what this question is asking:
Let B={v1, v2, v3} be a set of linearly independent vectors in R^3. Provev that B is a basis for R^3.
BASIS DEMANDS 2 THINGS
1.THEY SHOULD BE LINEARLY INDEPENDENT VECTORS IN THE DIMENSION GIVEN.
2.THEY SHOULD SPAN THE WHOLE SPACE UNDER CONSIDERATION.
HERE WE ARE GIVEN THAT V1,V2,V3 ARE LINEARLY INDEPENDENT IN R^3 AND IN R^3 THERE CAN BE 3 AND ONLY 3 INDEPENDENT VECTORS FORMING THE BASIS.SO THE ANSWER FOLLOWS FROM THIS AS WE HAVE ONLY 3 VECTORS AND THEY ARE INDEPENDENT.SO THAT PROVES IT.IF YOU WANT TO KNOW HOW THERE WILL BE ONLY 3 INDEPENDENT VECTORS SPANNING R^3 PLEASE COME BACK AND WE SHALL EXPLAIN.