Suppose that a 4 x 4 matrix A has eigenvalues g = 1, 12 = - 2, 13 = 3, and A4 = - 3. Use the following method to find det (A). If P(A) = det (AI - A) = A" + c1A" - 1 + ... + Cn So, on setting A = 0, we obtain that det (- A) = c, or det (A) = (- 1)^cn det (A) =
Suppose that a 4 x 4 matrix A has eigenvalues g = 1, 12 = - 2, 13 = 3, and A4 = - 3. Use the following method to find det (A). If P(A) = det (AI - A) = A" + c1A" - 1 + ... + Cn So, on setting A = 0, we obtain that det (- A) = c, or det (A) = (- 1)^cn det (A) =
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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Transcribed Image Text:Suppose that a 4 x 4 matrix A has eigenvalues A, = 1, , = - 2, 13 = 3, and A4 = - 3. Use the following method to find det (A).
If
p(A) = det (AI – A) = A" + c,A" - 1 + ... + Cn
So, on setting A = 0, we obtain that
det (- A) = cn or det (A) = (- 1)^cn
det (A) =
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