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Mathematics Question on Matrices

Let F: R3 ->R2 be the linear map defined by F(x, y, z) = (3x+2y-4z, x-5y+3z). The basis of R3 is S and basis of R2 is S', where S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)} and S' = {(1, 3), (2, 5)}. Then the matrix of F in the bases of R3 and R2 is

A

[−7−33−13 4198]\begin{bmatrix} -7 & -33 & -13\\\ 4 & 19 & 8 \end{bmatrix}

B

[−7−338 315−13]\begin{bmatrix} -7 & -33 & 8\\\ 3 & 15 & -13 \end{bmatrix}

C

[−74 −3319 1318]\begin{bmatrix} -7 & 4\\\ -33 & 19\\\ 13 & 18 \end{bmatrix}

D

[−713−33 4189]\begin{bmatrix} -7 & 13 & -33\\\ 4 & 18 & 9 \end{bmatrix}

Answer

[−7−33−13 4198]\begin{bmatrix} -7 & -33 & -13\\\ 4 & 19 & 8 \end{bmatrix}

Explanation

Solution

The correct answer is(A): [−7−33−13 4198]\begin{bmatrix} -7 & -33 & -13\\\ 4 & 19 & 8 \end{bmatrix}