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A²-6 + 11 = 0 1-3 2 5 and by the theorem you have A²-64 + 111₂ = 0 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05-1 Đ -15-1 00 1 STEP 1: Find and expand the characteristic equation. 2³-422-102-5=0 X STEP 2: Compute the required powers of A. 5 X 25 5 X 30 0 0 23 30 X 4 5 1 X 150 X 26 X X 175 X 30 X 0 ✓ 0 ✓ -1 X STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) 4³-44²-104-513=0| STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? Yes O No

A²-6 + 11 = 0 1-3 2 5 and by the theorem you have A²-64 + 111₂ = 0 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05-1 Đ -15-1 00 1 STEP 1: Find and expand the characteristic equation. 2³-422-102-5=0 X STEP 2: Compute the required powers of A. 5 X 25 5 X 30 0 0 23 30 X 4 5 1 X 150 X 26 X X 175 X 30 X 0 ✓ 0 ✓ -1 X STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) 4³-44²-104-513=0| STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? Yes O No

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. X²-6 + 11-0 A = 1-3 2 5 and by the theorem you have A² - 64 + 111₂ = O Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05-1 A-1 5-1 00 STEP 1: Find and expand the characteristic equation. 2³-42²-102-5=0| STEP 2: Compute the required powers of A. x 25 A² = 5 X 30 1 X |x 26 X X X 30 x 0 0 -1 x STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) 4³-44²-104-513 = 0 STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? ● Yes O No 0 23 30 0 150 175 X 4 5
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. X²-6 + 11-0 A = 1-3 2 5 and by the theorem you have A² - 64 + 111₂ = O Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05-1 A-1 5-1 00 STEP 1: Find and expand the characteristic equation. 2³-42²-102-5=0| STEP 2: Compute the required powers of A. x 25 A² = 5 X 30 1 X |x 26 X X X 30 x 0 0 -1 x STEP 3: Write a matrix version of the characteristic equation by replacing with A. (Use I for the 3x3 identity matrix.) 4³-44²-104-513 = 0 STEP 4: Substitute the powers of A into the matrix equation from step 3, and simplify. Is the matrix equation true? ● Yes O No 0 23 30 0 150 175 X 4 5
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