1 The Cayley-Hamilton Theorem gives us a method of finding powers of a matrix. For example, if A is a 2x2 matrix and has characteristic equation A²+bx+c=0 then A²+bA+cI = 0, hence A² = -bA - cI. (a) Verify this result for the matrix [29]. (b) By multiplying throughout by A we get A³ = -bA² - cA which can be evaluated using the result of part (a). Continue in this way to calculate A³ and A4.
1 The Cayley-Hamilton Theorem gives us a method of finding powers of a matrix. For example, if A is a 2x2 matrix and has characteristic equation A²+bx+c=0 then A²+bA+cI = 0, hence A² = -bA - cI. (a) Verify this result for the matrix [29]. (b) By multiplying throughout by A we get A³ = -bA² - cA which can be evaluated using the result of part (a). Continue in this way to calculate A³ and A4.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 41EQ:
In general, it is difficult to show that two matrices are similar. However, if two similar matrices...
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![1 The Cayley-Hamilton Theorem gives us a method of finding powers of a matrix. For example, if A is a 2x2
matrix and has characteristic equation λ² + bλ + c = 0 then A² + bA+cI = 0, hence A² = -bA - cI.
(a) Verify this result for the matrix [19].
(b) By multiplying throughout by A we get A³ -bA² CA which can be evaluated using the result of
part (a). Continue in this way to calculate A³ and A4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc3c0612-e198-45c8-8e80-98d06c0b64b4%2F7c9080f9-54c1-4a98-b6b0-5d65fda61209%2F3x9ox9c_processed.png&w=3840&q=75)
Transcribed Image Text:1 The Cayley-Hamilton Theorem gives us a method of finding powers of a matrix. For example, if A is a 2x2
matrix and has characteristic equation λ² + bλ + c = 0 then A² + bA+cI = 0, hence A² = -bA - cI.
(a) Verify this result for the matrix [19].
(b) By multiplying throughout by A we get A³ -bA² CA which can be evaluated using the result of
part (a). Continue in this way to calculate A³ and A4.
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