The eigenvalues of the system are r 1 = 0.5 + 1.5 i , and r 1 = 0.5 − 1.5 i .

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Answer 1

Question

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

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Consider the cones K = = {(x1, x2, x3) | € R³ : X3 ≥√√√2x² + 3x² M = = {(21,22,23) (x1, x2, x3) Є R³: x3 > + 2 3 Prove that M = K*. Hint: Adapt the proof from the lecture notes for finding the dual of the Lorentz cone. Alternatively, prove the formula (AL)* = (AT)-¹L*, for any cone LC R³ and any 3 × 3 nonsingular matrix A with real entries, where AL = {Ax = R³ : x € L}, and apply it to the 3-dimensional Lorentz cone with an appropriately chosen matrix A.

I am unable to solve part b.

Let M = M₁U M₂ UM3 and K M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8}, M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10}, M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6}, ¯ = cone {(1, 2), (1,3)†} ≤ R². (a) Determine the set E(M,K) of efficient points of M with respect to K. (b) Determine the set P(M, K) of properly efficient points of M with respect to K.

Answer 2

Question

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

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Answer 3

Question

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

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Answer 4

Question

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

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Answer 5

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

Answer 6

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

Answer 7

Chapter 9.1, Problem 22P

(a)

To determine

To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

Answer 8

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

Answer 9

(b)

To determine

To show: That the eigen vector ξ(1)=(53−3i).

Answer 10

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

Answer 11

(c)

To determine

To show: That y′=(P−1AP)y, where P is (503−3).

Answer 12

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

Answer 13

(d)

To determine

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

Answer 14

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Answer 15

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Answer 16

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Answer 17

Ch. 9.1 - Prob. 1P Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 7P Ch. 9.1 - Prob. 8P Ch. 9.1 - Prob. 9P Ch. 9.1 - Prob. 10P

The eigenvalues of the system are r 1 = 0.5 + 1.5 i , and r 1 = 0.5 − 1.5 i .

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To show: The eigenvalues of the system are r1=0.5+1.5i, and r1=0.5−1.5i.

To show: That the eigen vector ξ(1)=(53−3i).

To show: That y′=(P−1AP)y, where P is (503−3).

The value of P−1 and proved that (P−1AP)=(0.51.5−1.50.5), where P is (503−3).

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Chapter 9 Solutions