Question

Consider a transformation T: R^3 -- R^2 defined by
T( x1,x2,x3)= (2x1-3x2+x3, 4x3-x1)

(A) show that the tranformation, T, is linear.

(b) Find T( e1, e2,e3) using these, determine the standard matrix of the transformation.

(c) find the image of v=(2, 0, 1 ) under the linear mapping T as a linear comination of T(e1,e2,e3)

(d) is T one-to-one? Does Ta map R^3 onto R^2? Explain