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Mathematics Question on Matrices

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

[34 2−5]\begin{bmatrix} 3 & 4 \\\ 2 & -5 \end{bmatrix}

B

[3−5 43]\begin{bmatrix} 3 & -5 \\\ 4 & 3 \end{bmatrix}

C

[30 1−5]\begin{bmatrix} 3 & 0 \\\ 1 & -5 \end{bmatrix}

D

[12 34]\begin{bmatrix} 1 & 2 \\\ 3 & 4 \end{bmatrix}

Answer

[34 2−5]\begin{bmatrix} 3 & 4 \\\ 2 & -5 \end{bmatrix}

Explanation

Solution

The correct answer is(A): [34 2−5]\begin{bmatrix} 3 & 4 \\\ 2 & -5 \end{bmatrix}