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Find the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0).

User Chicout
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Final answer:

To find the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0), we need to first find the reflection matrix and then multiply it by the rotation matrix. The matrix that represents the combined transformation is M = [-1 0; 0 -1].

Step-by-step explanation:

To find the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0), we need to first find the reflection matrix and then multiply it by the rotation matrix.

The reflection in the line y=x can be represented by the matrix R = [0 1; 1 0].

The rotation by 90° anticlockwise about (0,0) can be represented by the matrix C = [0 -1; 1 0].

To find the matrix that represents the combined transformation, we multiply R and C: M = R * C = [0 1; 1 0] * [0 -1; 1 0] = [-1 0; 0 -1].

Therefore, the matrix that represents a reflection in the line y=x followed by a rotation by 90° anticlockwise about (0,0) is M = [-1 0; 0 -1].

User Drico
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