1. Let T : R n R m be the linear transformation T(x) = Ax,

where A is the matrix 1 1 2

A= 0 1 4

-2 0 4

(a) Determine the order m n of A.

(b) Find the image of the vector x = (1, 2, 5) under T.

(c) Determine whether the vector x from part (b) is in the image Im(T) of T.

(d) Is the vector y = (1, 2, 6) in the image Im(T) of T?

If so, find a specific vector x such that T(x) = y.

(e) How many vectors x are possible in part (d)?

What does this say about y in relation to the columns of A?