he Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. 12 - 6À + 11 = 0 and by the theorem you have A2 - 6A + 111, = 0 1 -3 A emonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 4 A = 14 -1 TEP 1: Find and expand the characteristic equation. TEP 2: Compute the required powers of A. A² = TEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) TEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? O Yes O No
he Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. 12 - 6À + 11 = 0 and by the theorem you have A2 - 6A + 111, = 0 1 -3 A emonstrate the Cayley-Hamilton Theorem for the matrix A given below. 0 4 A = 14 -1 TEP 1: Find and expand the characteristic equation. TEP 2: Compute the required powers of A. A² = TEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) TEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? O Yes O No
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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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.
2 - 61 + 11 = 0
and by the theorem you have
A2 - 6A + 111, = 0
A =
2 5
Demonstrate the Cayley-Hamilton Theorem for the matrix A given below.
0 4
1
A =
1 4 -1
STEP 1: Find and expand the characteristic equation.
STEP 2: Compute the required powers of A.
A² =
A =
STEP 3: Write a matrix version of the characteristic equation by replacing i 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?
O Yes
O No
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