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4.5 EXERCISES The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1–11. [: 2 –1 А B = 3 p(t) = (t – 3)(t – 1), p(t) = (t 2)?, -6 –1 -7 4 -3 C = 3 2 0 D = 8 -3 3 -14 -2 5 32 –16 13 p(t) = -(t – 1)²(t + 1), p(t) = -(t – 1)³, 6 4 4 1 1 -1 -1 4 6 1 4 -1 1 -1 -1 E: F = 4 1 6 4 -1 –1 1 -1 1 4 4 6 -1 -1 -1 1 p(t) = (t + 1)(t + 5)2(t – 15), p(t) = (t + 2)(t – 2)3 In Exercises 1–11, find a basis for the eigenspace E, for the given matrix and the value of A. Determine the algebraic and geometric multiplicities of 2. 1. A, λ3 2. A, λ 1 3. В, А — 2

4.5 EXERCISES The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1–11. [: 2 –1 А B = 3 p(t) = (t – 3)(t – 1), p(t) = (t 2)?, -6 –1 -7 4 -3 C = 3 2 0 D = 8 -3 3 -14 -2 5 32 –16 13 p(t) = -(t – 1)²(t + 1), p(t) = -(t – 1)³, 6 4 4 1 1 -1 -1 4 6 1 4 -1 1 -1 -1 E: F = 4 1 6 4 -1 –1 1 -1 1 4 4 6 -1 -1 -1 1 p(t) = (t + 1)(t + 5)2(t – 15), p(t) = (t + 2)(t – 2)3 In Exercises 1–11, find a basis for the eigenspace E, for the given matrix and the value of A. Determine the algebraic and geometric multiplicities of 2. 1. A, λ3 2. A, λ 1 3. В, А — 2

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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4.5 EXERCISES The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1–11. 2 –1 A B = 3 p(t) = (t – 3)(t – 1), p(t) = (t – 2)², -6 –1 -7 4 -3 C = 3 2 0 D = 8 -3 3 -14 -2 5 32 –-16 13 p(t) = -(t – 1)²(t + 1), p(t) = -(t – 1)³, 6 4 4 1 1 -1 -1 4 6 1 4 -1 1 -1 –1 E F = 4 1 6 4 -1 –1 1 -1 1 4 4 6 -1 -1 –1 1 p(t) = (t + 1)(t + 5)²(t – 15), p(t) = (t +2)(t – 2)3 In Exercises 1–11, find a basis for the eigenspace E, for the given matrix and the value of A. Determine the algebraic and geometric multiplicities of A. 1. A, λ3 2. A, λ 1 3. В, А — 2
Transcribed Image Text:4.5 EXERCISES The following list of matrices and their respective char- acteristic polynomials is referred to in Exercises 1–11. 2 –1 A B = 3 p(t) = (t – 3)(t – 1), p(t) = (t – 2)², -6 –1 -7 4 -3 C = 3 2 0 D = 8 -3 3 -14 -2 5 32 –-16 13 p(t) = -(t – 1)²(t + 1), p(t) = -(t – 1)³, 6 4 4 1 1 -1 -1 4 6 1 4 -1 1 -1 –1 E F = 4 1 6 4 -1 –1 1 -1 1 4 4 6 -1 -1 –1 1 p(t) = (t + 1)(t + 5)²(t – 15), p(t) = (t +2)(t – 2)3 In Exercises 1–11, find a basis for the eigenspace E, for the given matrix and the value of A. Determine the algebraic and geometric multiplicities of A. 1. A, λ3 2. A, λ 1 3. В, А — 2
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