Question

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. \(\begin{bmatrix} -7 & -33 & -13\\   4 & 19 & 8 \end{bmatrix}\)
• B. \(\begin{bmatrix} -7 & -33 & 8\\   3 & 15 & -13 \end{bmatrix}\)
• C. \(\begin{bmatrix} -7 & 4\\   -33 & 19\\  13 & 18 \end{bmatrix}\)
• D. \(\begin{bmatrix} -7 & 13 & -33\\   4 & 18 & 9 \end{bmatrix}\)

Answer 1

The Correct Option is A

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