SOLUTION: Consider the following two vectors in R3 : u=(1,2,3) and v=(2,3,1). Show whether it is possible to express the vector w=(2,4,5) as a linear combination of u and v.

Algebra ->  College  -> Linear Algebra -> SOLUTION: Consider the following two vectors in R3 : u=(1,2,3) and v=(2,3,1). Show whether it is possible to express the vector w=(2,4,5) as a linear combination of u and v.      Log On


   



Question 929970: Consider the following two vectors in R3
: u=(1,2,3) and v=(2,3,1). Show whether it is possible to
express the vector w=(2,4,5) as a linear combination of u and v.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a(1,2,3)+b(2,3,1)=(2,4,5)
.
.
.
1.a%2B2b=2
2.2a%2B3b=4
3.3a%2Bb=5
There is no solution for these three equations in two unknowns.
No, it is not possible to form w as a linear combination of u and v.