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
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.
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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