Answer: Vector b is not a linear combination
Step-by-step explanation:
First of all we put the vectors in terms of different variables, such as:
a1(1,-2,0)=(a,-2a,0);
a2(0,1,3)=(0,b,3b);
a3(6,-6,18)=(6c,-6c,18c);
To know that a vector is a linear combination we need to express it like a sum of other different vectors.
(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)
(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)
We express this sum like a system of equations.
a+6c=2
-2a+b-6c=-2
3b+18c=6
We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.
