(Linear Algebra)12.7.1Pls help thanks 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 -312 - 61 + 11 = 0A =2and by the theorem you have5A2 - 6A + 111, = 0Demonstrate the Cayley-Hamilton Theorem for the matrix A given below.05 -1A =1 3-10 01STEP 1: Find and expand the characteristic equation.STEP 2: Compute the required powers of A.5A²1A3 =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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Answered: The Cayley-Hamilton Theorem states that…

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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(Linear Algebra)

12.

7.1

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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.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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