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Given the plane: x-y in 3-space do the following: a) show the normal vector b) construct a matrix that will reflect points across this plane c) Compute the eigenvalues for this matrix d) compute the eigenvectors for these eigenvalues

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Given the plane: x-y in 3-space do the following:

a) show the normal vector

b) construct a matrix that will reflect points across this plane

c) Compute the eigenvalues for this matrix

d) compute the eigenvectors for these eigenvalues