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Mathematics Question on Matrices

Let A =[23\4−1]\begin{bmatrix}2&3\\\4&-1\end{bmatrix} then the matrix B that represents the linear operator A relative to the basis
S = {u1,u2u_1,u_2}=[1,3]T,[2,5]T{[1, 3]^T, [2, 5]^T}, is:

A

[5389\3254]\begin{bmatrix}53&89\\\32&54\end{bmatrix}

B

[−53−89\3254]\begin{bmatrix}-53&-89\\\32&54\end{bmatrix}

C

[5355\9823]\begin{bmatrix}53&55\\\98&23\end{bmatrix}

D

[53−23\8945]\begin{bmatrix}53&-23\\\89&45\end{bmatrix}

Answer

[−53−89\3254]\begin{bmatrix}-53&-89\\\32&54\end{bmatrix}

Explanation

Solution

The correct option is(B)