Question

Find det (A) given that A has $p(lambda)$ as its characteristic polynomial. $p(lambda) = lambda^3 - 8lambda^2 + lambda + 7$ det (A) = Hint: See the proof of Theorem 7.1.4. (If given det $(lambda I - A) = lambda^n + c_1lambda^{n-1} + ... + c_n$ then, on setting $lambda = 0$, det $(-A) = c_n$ or $(-1)^n$det (A) = $c_n$)

          Find det (A) given that A has $p(lambda)$ as its characteristic polynomial.
$p(lambda) = lambda^3 - 8lambda^2 + lambda + 7$
det (A) = 
Hint: See the proof of Theorem 7.1.4.
(If given det $(lambda I - A) = lambda^n + c_1lambda^{n-1} + ... + c_n$ then, on setting $lambda = 0$, det $(-A) = c_n$ or $(-1)^n$det (A) = $c_n$)

Find det (A) given that A has p(lambda) as its characteristic polynomial.
p(lambda) = lambda^3 - 8lambda^2 + lambda + 7
det (A) =
Hint: See the proof of Theorem 7.1.4.
(If given det (lambda I - A) = lambda^n + c1lambda^n-1 + ... + cn then, on setting lambda = 0, det (-A) = cn or (-1)^ndet (A) = cn)

Added by Anita S.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Subhadeepta Sahoo

01/03/2022

Step 1

Step 1: Given the characteristic polynomial of matrix A as $ p(\lambda) = \lambda^3 - 8\lambda^2 + \lambda + 7 $. Show more…

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Find det (A) given that A has p(λ) as its characteristic polynomial. p(λ) = λ^3 - 8λ^2 + λ + 7 det (A) Hint: See the proof of Theorem 7.1.4. ( If given det (αl - A) = λ^n + c1λ^n-1 + ... + cn then, on setting λ = 0, det (- A) = cn or (- 1)^ndet (A) = cn )