16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 6.2.4

Elementary Canonical Forms

Mathematics — Linear Algebra · diagonalizability

Problem

Let TT be the linear operator on R3R^3 which is represented in the standard ordered basis by the matrix [−944−834−1687].\begin{bmatrix} -9 & 4 & 4 \\ -8 & 3 & 4 \\ -16 & 8 & 7 \end{bmatrix}. Prove that TT is diagonalizable by exhibiting a basis for R3R^3, each vector of which is a characteristic vector of TT.

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