Question

Determine whether (1,2,3) is a linear combination of (1,0,1) and (2,1,0).

Answer 1

no. in order for (1, 2, 3) to be a linear comb. of the two vectors, there has to exist a and b such that a*(1,0,1) + b*(2,1,0) = (1,2,3) or
a + 2b = 1
0a + b = 2
a + 0b = 3