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The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. A²6λ + 11 = 0 1 -3 A = and by the theorem you have A²6A + 111₂ = 0 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 02 -1 A = -1 4 1 0 0 -1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. A² = A³ =

The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. A²6λ + 11 = 0 1 -3 A = and by the theorem you have A²6A + 111₂ = 0 2 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 02 -1 A = -1 4 1 0 0 -1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. A² = A³ =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. A²6λ + 11 = 0 1 -3 A = and by the theorem you have 2 5 A² - 6A + 111₂ = 0 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 4 1 0 0 -1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. A² A³ = 100 100 LOO DC
Transcribed Image Text:The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. A²6λ + 11 = 0 1 -3 A = and by the theorem you have 2 5 A² - 6A + 111₂ = 0 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 2 -1 A = -1 4 1 0 0 -1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. A² A³ = 100 100 LOO DC
STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? Yes No
Transcribed Image Text:STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? Yes No
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