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Consider the matrix A = Go). Somebody tells you that powers of A (i.e. A, A², A³, etc.) follow the same pattern as powers of i (i, i², i³, etc.). Are they right? Why or why not? (Note that i refers to the square root of –1, not tne identity r atri: The identity matrix is I.)

Consider the matrix A = Go). Somebody tells you that powers of A (i.e. A, A², A³, etc.) follow the same pattern as powers of i (i, i², i³, etc.). Are they right? Why or why not? (Note that i refers to the square root of –1, not tne identity r atri: The identity matrix is I.)

Advanced Engineering Mathematics
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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1 Consider the matrix A = G): Somebody tells you that powers of A (i.e. A, A², A³, etc.) follow the same pattern as powers of i (i, i², i³, etc.). Are they right? Why or why not? (Note that i refers to the square root of –1, not tne identity r atri. The identity matrix is I.)
Transcribed Image Text:1 Consider the matrix A = G): Somebody tells you that powers of A (i.e. A, A², A³, etc.) follow the same pattern as powers of i (i, i², i³, etc.). Are they right? Why or why not? (Note that i refers to the square root of –1, not tne identity r atri. The identity matrix is I.)
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