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:

• A. \(\begin{bmatrix} 3 & 4 \\   2 & -5  \end{bmatrix}\)
• B. \(\begin{bmatrix} 3 & -5 \\   4 & 3  \end{bmatrix}\)
• C. \(\begin{bmatrix} 3 & 0 \\   1 & -5  \end{bmatrix}\)
• D. \(\begin{bmatrix} 1 & 2 \\   3 & 4  \end{bmatrix}\)

Answer 1

The Correct Option is A

The correct answer is(A): \(\begin{bmatrix} 3 & 4 \\   2 & -5  \end{bmatrix}\)