Consider this matrix transformation: [[0,-1],[1,0]] What is the geometric effect of this transformation? Choose 1 answer: A A reflection across the y axis B A reflection across the line y=x (c) A rotation about the origin by 90^(@) (D) A rotation about the origin by 180^(@)

Question

Consider this matrix transformation:  [[0,-1],[1,0]] What is the geometric effect of this transformation? Choose 1 answer: A A reflection across the  y axis B A reflection across the line  y=x (c) A rotation about the origin by  90^(@) (D) A rotation about the origin by  180^(@)

Bytelearn · Accepted Answer

Identify transformation: Identify the matrix transformation. The matrix given is: [[0,-1],  [1, 0]] This is a 2x2 matrix that can be applied to vectors in the plane.Effect on basis vectors: Understand the effect of the matrix on basis vectors. To understand the transformation, we can look at what happens to the standard basis vectors i = [1, 0] and j = [0, 1]. Applying the matrix to i: [[0,-1],  [1, 0]] * [1,              0] = [0,                     1] The vector i is rotated 90 degrees counterclockwise to become j.Apply to basis vectors: Apply the matrix to the second basis vector j: [[0,-1],  [1, 0]] * [0,              1] = [-1,                     0] The vector j is rotated 90 degrees counterclockwise to become -i.Conclude geometric effect: Conclude the geometric effect of the transformation. Both basis vectors are rotated 90 degrees counterclockwise. Therefore, the matrix represents a rotation by 90 degrees counterclockwise about the origin.

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