Problems 28 through 30 develop a method of computing powers of a square matrix. If then show
Question:
Problems 28 through 30 develop a method of computing powers of a square matrix.
If
then show that
where I denotes the 2 x 2 identity matrix. Thus every 2 x 2 matrix A satisfies the equation
where det A = ad - bc denotes the determinant of the matrix A, and trace A denotes the sum of its diagonal elements. This result is the 2-dimensional case of the Cayley- Hamilton theorem of Section 6.3.
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Related Book For 
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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