MATH221 April 2009
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Question 07 (b)
Let be the reflection across the line , and let A be the standard matrix of this linear transformation.
Find the matrix A.
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From part (a), we know that 1 is an eigenvalue of A with eigenvector , and -1 is an eigenvalue of A with eigenvector .
If we form the matrix whose columns are the eigenvectors, with corresponding diagonal matrix , we know that the matrix A decomposes via the standard matrix diagonalization
Upon computing , we multiply the three matrices together to find A:
As a quick check of our work, we should verify that indeed
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