Show that if A is an n x n matrix, then A" can be written as a linear combination of the matrices I, A, A², . . , A" = a0I + a1A+¤2A² + An-1; that is, there are scalars ao, ɑ1, a2, . .. , an-1 such that + an-14"-1.
Show that if A is an n x n matrix, then A" can be written as a linear combination of the matrices I, A, A², . . , A" = a0I + a1A+¤2A² + An-1; that is, there are scalars ao, ɑ1, a2, . .. , an-1 such that + an-14"-1.
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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Hint: Cayley-Hamilton Theorem
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