?Distinct Eigenvalues Extended Extend the proof of the Distinct Eigenvalue Theorem for a
Chapter 5, Problem 36(choose chapter or problem)
Distinct Eigenvalues Extended Extend the proof of the Distinct Eigenvalue Theorem for a \(3 \times 3\) matrix A as follows: Show that if A has 3 distinct eigenvalues λ1, λ2, λ3, then the corresponding eigenvectors \(\bar{v}_{1}, \bar{v}_{2}, \bar{v}_{3}\) are linearly independent. HINT: Use the fact that an eigenvectors \(\bar{v}_{1}\) cannot be zero, and follow the steps shown in the proof for two distinct eigenvalues.
Equation Transcription:
Text Transcription:
3 times 3
bar v_1 , bar v_2 , bar v_3
bar v_1
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