Math Problem Statement

Diagonalize (if possible) each of the following matrices. Give the similarity transformation. (Let D = C−1AC. Enter sqrt(n) for √n. If an answer does not exist, enter DNE in any cell of the matrix.) (a)

11 5 −5

−1 1 1 9 5 −3 [C D] =

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Diagonalization
Eigenvalues
Eigenvectors

Formulas

Determinant of matrix A: det(A - λI) = 0
Similarity transformation: D = C^{-1}AC
Eigenvector equation: (A - λI)v = 0

Theorems

Eigenvalue Theorem
Diagonalization Theorem
Cayley-Hamilton Theorem

Suitable Grade Level

Undergraduate (Math or Engineering)