For each of the following ODEs determine if the eigenvalues are (a) real and distinct, (b) repeated, (c) complex conjugate pairs: 1. +2x+3x = 0 2. 3. 4. + 4x + x = 0 + 4x + 4x = 0 + 3x = 0

Q: Let A = [a = [a b]. Find a formula for for the eigenvalues of A in terms of a, b, c and d.

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Q: Find the eigenvalues and the eigenvectors of A and A²: A 1 3 = 2 0 λι 2 = A² = 2 -31 6 λι 2 with X1…

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. -4 -2 = -11, x, =…

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Q: Let A = O 2√6 00 O-2 02 Note that the quadratic formula = O -1 2 3 -2√6 Find the sum of all…

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Q: When the eigenvalues of a b A = are 11 = 4 and 12 = 0, what are the possible values of a and d?…

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Q: AX1 AX2 -4-2 3 1 СЕВЕ -2-7 6 2 1 2 6 -1 -4 -2 3 -2 -7 6 1 2-6 -4 -2 3 -2-7 6 1 2 6 Ax3 = 0 3 100 JT…

A: Here we have to verify that λi  is an eigenvalue of A and that xi is a corresponding eigenvector .

Q: Can step 2 be more elaborated upon? Specifically on how each eigenspace is found.

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Q: Exercise 6.2.1 For each system of ODE in (a)-(g), do the following: • Formulate the system as x =…

A: According to the guidelines, only one question and maximum three subpart can be answered. Please…

Q: Use the eigen-pair A = 1, v = |I to decide which of these is a solution to d 1 dt -3 1 -1/3 t et t…

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Q: 4.- Eigenvalues and Eigenvectors. Calculate the characteristic polynomius, the Eigenvalues, each one…

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Q: Use Ackermann's Formula to find the observer gain L so that the eigenvalues of A-LC are placed at -3…

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Q: eigenvalues 4 - 2 1 0 -1 Tota- 23 3 -2 -3 4 2 1 0 1-11 -2 5 -2 3 -2 - 1 1 -2 4

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Q: 04) Find the eigenvalues of A, B, and C: 2 3 A = 0 4 5 0 6 --E] - -- - --) To o 1 and B =0 2 0 3 0 2…

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Q: When the eigenvalues of a b A = 0 d are 11 = 2 and 12 = 0, what are the possible values of a and d?…

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Q: For 6-9, let A=0 I Answer for #8&9 6.) Find the characters polynomial A [10 – a -9 41= (10 – a) x (2…

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Q: Find the eigenvalues and the eigenvectors of these two matrices: A λ1 - = 2 3 A+ I = λι 12 = and…

A: Step 1:Step 2:Step 3:Step 4:

Q: When the eigenvalues of A = are 11 = 3 and 1, = 0, what are the possible values of a and d? (Select…

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Q: x1 = -x2, x2 = 6x₁5x2 with x₁ (0) = 2 and x₂ (0) = 5. (O) Dand (0)

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: that are close to -4

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Q: For matrix C, find the associated eigenvalues. c=[-5₁ 3 C -1 O1 and 5 O4 and 3 O-5 and 2 O4 and 6

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