Question:
Consider the linear mapping F: R2 →R2 defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R2: E= {e1, e2} = {(1, 0), (0, 1)} and S = {u1, u2} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:
Consider the linear mapping F: R2 →R2 defined by F(x, y) = (3x+4y, 2x-5y) and following bases of R2: E= {e1, e2} = {(1, 0), (0, 1)} and S = {u1, u2} = {(1, 2), (2, 3)}. Then the matrix A representing F relative to the basis E is:
Updated On: Mar 12, 2025
- \(\begin{bmatrix} 3 & 4 \\ 2 & -5 \end{bmatrix}\)
- \(\begin{bmatrix} 3 & -5 \\ 4 & 3 \end{bmatrix}\)
- \(\begin{bmatrix} 3 & 0 \\ 1 & -5 \end{bmatrix}\)
- \(\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}\)
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The Correct Option is A
Solution and Explanation
The correct answer is(A): \(\begin{bmatrix} 3 & 4 \\ 2 & -5 \end{bmatrix}\)
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