The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic eguation. For example, the characteristic equation of the matrix shown below is as follows. 1 -3 22 - 61 + 11 = 0 and by the theorem you have A = 2 A2 - 6A + 111,2 = 0 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05 -1 A = 1 3 -1 0 0 1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. 5 A² = 1 A3 = STEP 3: Write a matrix version of the characteristic equatian huronlasisai with A. (Use I for the 3x3 identity matrix.) Enter an exact number.
The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic eguation. For example, the characteristic equation of the matrix shown below is as follows. 1 -3 22 - 61 + 11 = 0 and by the theorem you have A = 2 A2 - 6A + 111,2 = 0 5 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 05 -1 A = 1 3 -1 0 0 1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of A. 5 A² = 1 A3 = STEP 3: Write a matrix version of the characteristic equatian huronlasisai with A. (Use I for the 3x3 identity matrix.) Enter an exact number.
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.
--[:)
1 -3
12 - 61 + 11 = 0
A =
2
and by the theorem you have
5
A2 - 6A + 111, = 0
Demonstrate the Cayley-Hamilton Theorem for the matrix A given below.
05 -1
A =
1 3
-1
0 0
1
STEP 1: Find and expand the characteristic equation.
STEP 2: Compute the required powers of A.
5
A²
1
A3 =
STEP 3: Write a matrix version of the characteristic egie hanlasinai with A. (Use I for the 3x3 identity matrix.)
Enter an exact number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4391da0a-9374-45f8-a9c6-851f56bfed48%2Fd59416c3-7428-41c4-b851-d000d694e044%2Ffranibf_processed.png&w=3840&q=75)
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.
--[:)
1 -3
12 - 61 + 11 = 0
A =
2
and by the theorem you have
5
A2 - 6A + 111, = 0
Demonstrate the Cayley-Hamilton Theorem for the matrix A given below.
05 -1
A =
1 3
-1
0 0
1
STEP 1: Find and expand the characteristic equation.
STEP 2: Compute the required powers of A.
5
A²
1
A3 =
STEP 3: Write a matrix version of the characteristic egie hanlasinai with A. (Use I for the 3x3 identity matrix.)
Enter an exact number.
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