Suppose that A is a diagonalizable matrix that has been written in the form A = PDP-1,
Question:
(a) Show that for positive integer k, Ak = PDkP-1.
(b) Use the result of part (a) to compute A50° for
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(c) Show that if D is diagonal, then Dk is diagonal.
(d) Is the equation in part (a) true for k = -1? Could this be useful in finding the inverse of a matrix?
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a Informal Proof If A PDP 1 then Alternatively this proposition can be ...View the full answer
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Related Book For 
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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