linear combination of the basis vectors

Question

Consider the set of vectors in R3 given by a1=(1, 0, 0), a2=(1,-2,0), a3=(0,0,1).

Write the vector x=(1, 2, 5) as a linear combination of the basis vectors a1, a2, a3.

Answer 1

(1,2,5) = a(1,0,0) + b(1,-2,0) + c(0,0,1)

a + b = 1

-2b = 2

c = 5

So, c = 5, b = -1, and a = 2

(1,2,5) = 2(1,0,0) -1(1,-2,0) +5(0,0,1)