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A matrix A € M4 (R) has rank 2. Which of the following cannot be the characteristic polynomial of A? Explain your answer. p(t) = t¹ + 6t, q(t) = t¹ + 6t², r(t) = t¹ + 6t³ (Hint: what does null A have to do with the characteristic polynomial?)

A matrix A € M4 (R) has rank 2. Which of the following cannot be the characteristic polynomial of A? Explain your answer. p(t) = t¹ + 6t, q(t) = t¹ + 6t², r(t) = t¹ + 6t³ (Hint: what does null A have to do with the characteristic polynomial?)

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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Confused about how to determine it is a character polynimal. Thank you!

A matrix A € M₁(R) has rank 2. Which of the following cannot be the characteristic polynomial of A? Explain your answer. p(t) = t¹ + 6t, q(t) = t¹ + 6t², r(t) = t² + 6t³ (Hint: what does null A have to do with the characteristic polynomial?)
Transcribed Image Text:A matrix A € M₁(R) has rank 2. Which of the following cannot be the characteristic polynomial of A? Explain your answer. p(t) = t¹ + 6t, q(t) = t¹ + 6t², r(t) = t² + 6t³ (Hint: what does null A have to do with the characteristic polynomial?)
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