Find the eigenvalues and eigenvectors of the linear transformation T: R² R² whose matrix relative to the standard basis of R² is - (-¹2-²) A = Use your answer to (a) to find a basis for R² consisting of eigenvectors of T. Write down matrix of T relative to this basis of eigenvectors. Let T: R³ R³ be the function that rotates each point in R³ through an angle = al the z-axis. Explain briefly why T is linear. Find the matrix of T relative to the standard of R³.

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