Question

In R^3 we have a = (1, 0,-2); b = (-1, 3, 1) and we consider x = a + b; y = -2a + b and z =3a – 5b.

Using the properties of the vector space, calculate T = 2x – 3y + z.

Answer 1

$$2x – 3y + z=2(a+b) – 3(-2a+b) + 3a-5b$$

$$=2a+2b+6a-3b+3a-5b=11a-6b$$

$$=11(1,0,-2)-6(-1,3,1)=(17, -18, -28)$$

$$T=(17, -18, -28)$$