Consider this matrix transformation: [[-1,0],[0,1]] 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^(@)

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Consider this matrix transformation:  [[-1,0],[0,1]] 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^(@)

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Identify Matrix Elements: Identify the matrix and its elements. The given matrix is: $$ \begin{bmatrix} -1 & 0 \ 0 & 1 \end{bmatrix} $$ This is a 2x2 matrix with elements a11 = -1, a12 = 0, a21 = 0, and a22 = 1.Effect on Basis Vectors: Analyze the effect of the matrix on the basis vectors. The effect of the matrix on the x-axis basis vector (1,0) is: $$ \begin{bmatrix} -1 & 0 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 1 \ 0 \end{bmatrix} = \begin{bmatrix} -1 \ 0 \end{bmatrix} $$ This means that the x-axis basis vector is reflected across the y-axis.Effect on x-axis: Analyze the effect of the matrix on the y-axis basis vector. The effect of the matrix on the y-axis basis vector (0,1) is: $$ \begin{bmatrix} -1 & 0 \ 0 & 1 \end{bmatrix} \begin{bmatrix} 0 \ 1 \end{bmatrix} = \begin{bmatrix} 0 \ 1 \end{bmatrix} $$ This means that the y-axis basis vector remains unchanged.Effect on y-axis: Determine the geometric effect of the transformation. Since the x-axis basis vector is reflected across the y-axis and the y-axis basis vector remains unchanged, the overall effect of the transformation is a reflection across the y-axis.

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