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The linear operator T: R^3 R^3 defined by T(x_1, x_2, x_3) = (x_1 - 3x_3, x_1 + 2x_2 + x_3, x_3 - 3x_1). Determine whether or not there is a basis F for R^3 relative to which the transformation T can be represented by a diagonal matrix D=[T]_F. If there is, show that D is similar to the standard matrix representation [T]_E. If not, why? Show work.
R^3: is Euclidean 3-space
Diagonalization of a matrix is investigated. The solution is well presented.