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    IBHardVectors10–12

    Matrix Transformations

    Transformações Matriciais

    The matrix M=(0−110)M = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} represents a transformation. What geometric transformation does MM represent? Find the image of the point (3,5)(3, 5) under MM.

    Apply MM to the point (3,5)(3,5): multiply the matrix by the column vector.

    Solution

    Step 1 of 3

    1. 1.M×(3,5)=(0×3+(−1)×5,1×3+0×5)=(−5,3)M \times (3, 5) = (0 \times 3 + (-1) \times 5, 1 \times 3 + 0 \times 5) = (-5, 3)