Answer to Question #316831 in Linear Algebra for babyG

Question

Answer the following questions:

a) Let T be a linear transformation from R2 to R2 such that

 ⟶   [ 1                     ⟶    [ 2

T(u) = -1 ]          and T(u) =  3 ]                            <--Vectors

                  ⟶    ⟶

Compute T(3u - 2w).

b) Consider the matrix

     [ 1 -4 7 -5

A =   0  1 -4 3

       2 -6 6 -4 ]

       ⟶    ⟶      ⟶   [ -1

Let T(x) - Ax and b =   -1                   

                                   0 ]

                         ⟶                 ⟶   ⟶

Is there a vector x such that T(x) = b? Justify your answer.