Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are X₁ = -2, A₂ = 3, and A3 = 4. If V₁ = [1 0 0], V2 = [1 1 0], V3 = [011] are eigenvectors of A corresponding to A₁, A2, and A3, respectively, then factor A into a product PDP-1 with D diagonal, and use this factorization to find A5. A5 =
Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are X₁ = -2, A₂ = 3, and A3 = 4. If V₁ = [1 0 0], V2 = [1 1 0], V3 = [011] are eigenvectors of A corresponding to A₁, A2, and A3, respectively, then factor A into a product PDP-1 with D diagonal, and use this factorization to find A5. A5 =
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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![Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are ₁ = −2, A₂ = 3, and A3
= 4. If
V₁ = [1 0 0], V2 = [1 1 0], V3 = [011]
are eigenvectors of A corresponding to A₁, A2, and A3, respectively, then factor A into a product PDP-¹ with D diagonal, and use this
factorization to find A5.
A5
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe70859f-d1ee-4d19-93f5-d3c21b44393e%2Feb585d6c-4e51-498e-9577-a03328d582f0%2Fhf7mzvd_processed.png&w=3840&q=75)
Transcribed Image Text:Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are ₁ = −2, A₂ = 3, and A3
= 4. If
V₁ = [1 0 0], V2 = [1 1 0], V3 = [011]
are eigenvectors of A corresponding to A₁, A2, and A3, respectively, then factor A into a product PDP-¹ with D diagonal, and use this
factorization to find A5.
A5
=
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