Find the best answer and explain why

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Find the best answer and explain why.

1. Consider the linear map T: R³ → R³ given by T(x, y, z) = (x−2y−2z,2x−6y−7z,−4x+10y+10z).

Using the basis (5,4,−2),(0,1,−1), (1, 3/2, −1) for the domain and the standard basis for the codomain, the first row of the matrix for T is

(a) (1,0,0)

(b) (1,2,−4)

(c) (5,4,−2)

(d) (1,−2,−2)

(e) (5,0,1)

2. Consider the linear map T: R³ → R³ given by T(x, y, z) = (x−2y−2z,2x−6y−7z,−4x+10y+10z).

Using the standard basis for the domain and the standard basis for the codomain, the first row of the matrix for T is

(a) (1,0,0)

(b) (1,2,−4)

(c) (5,4,−2)

(d) (1,−2,−2)

(e) (5,0,1) 

3. Using the basis (x−1), (x−2) for P₁(R), the matrix M(x−5) is

(a) (9/2 ,−4 )

(b) (3, 2, 1)

(c) (−3,4)

(d) (1, 0,−1)

(e) (8,−3)