Math Problem Statement

Find both eigenvalues λ1 and λ2 and corresponding eigenvectors X1 and X2 of the matrix A = [[5, 0], [6, -1]]. Ensure λ1 < λ2, and X1 corresponds to λ1.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Eigenvalues and Eigenvectors

Formulas

Determinant equation det(A - λI) = 0
Eigenvector equation (A - λI)X = 0

Theorems

Eigenvalue theorem
Diagonalization

Suitable Grade Level

Undergraduate Mathematics or Linear Algebra Course

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