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
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
Updated On: Feb 13, 2025
- \(\begin{bmatrix} -7 & -33 & -13\\ 4 & 19 & 8 \end{bmatrix}\)
- \(\begin{bmatrix} -7 & -33 & 8\\ 3 & 15 & -13 \end{bmatrix}\)
- \(\begin{bmatrix} -7 & 4\\ -33 & 19\\ 13 & 18 \end{bmatrix}\)
- \(\begin{bmatrix} -7 & 13 & -33\\ 4 & 18 & 9 \end{bmatrix}\)
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The Correct Option is A
Solution and Explanation
The correct answer is(A): \(\begin{bmatrix} -7 & -33 & -13\\ 4 & 19 & 8 \end{bmatrix}\)
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