Problem 2.

Let the 3 vectors, a1, a2, b be given below.

(a) Is b a linear combination of a1 and a2? If so, write the linear combination explicitly (using numbers).

a1 := matrix([[1], [2], [-1]])

a2 := matrix([[2], [-1], [3]])

b := matrix([[5], [-2], [7]])

(b) Are the vectors a1 and a2 linearly independent? Give a reason.

(c) Let A be the matrix with columns a1 and a2. If A is the standard matrix of a linear

transformation T, is T one to one? Show and explain why.

(d) Let M be the matrix with columns a1, a2, b. If M is the standard matrix of a linear

transformation S, is S onto? Show and explain why.