If A is an (n x n)-matrix of real constants that has a complex eigenvalue and eigenvector v, then the real and imaginary parts of w(t) = elty are linearly independent real-valued solutions of x'=Ax: X₂(t)= Im(w(t)), The matrix in the following system has complex eigenvalues; use the above theorem to find the general (real-valued) solution. 030 -3 0 0 x 005 x(t) = X'= Find the particular solution given the initial conditions. x(t) = x(0) = X₁(t) = Re(w(t)) and

Q: Let Q(x) = 7x} +x} +7x} – 8x1x2 – 4x1x3 – 8x2x3. Find a unit vector x in R3 at which Q(x) is…

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Q: Suppose the 3 × 3 matrix A has eigenvalues λ1 = −6, λ2 = −2, and λ3 = 5.

A: according to guidelines we can solved only first 3 subparts thank you   We have the eigen values of…

Q: The 2×2 real symmetric matrix A has two distinct eigenvalues λ1 and λ2. (a) If v1 =(a,b) is an…

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Q: [a b] c d 3: Let A = be a singular matrix with trA = 4. Find all eigenvalues of A. Hint: Think about…

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Q: I need the eigenvalues and eigenvectors of the matrix A = [2 0 3 2 ]

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Q: (b) Assume two 3×3 matrices A and B have exactly the same characteristics equations. Let A have…

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Q: What is the eigenvalue of the operator T, given by T(x) = 3x + 2, for the vector x = [1, 2]?

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Q: The eigenvalues of a 3x3 matrix A are -4,2,9. Find the determinant of (A-1)T

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Q: The 2×2 real symmetric matrix A has two distinct eigenvalues λ1 and λ2.If v1 =(1,2) is an…

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Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 4i and corresponding eigenvector * = [-…

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Q: Let A be 2 x 2 matrix with trace(A) = 5 and det(A) = what is the value of 4X₁ +8X₂ ? tr(A) = = 5 ve…

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Q: (c) Find f(A), where f(t) = tª – 4t3 + 3t – 7.

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Q: Let Q(x) = 143x² – 34x2 – 34x² – 36x1x2 – 36x1x3 — 72x2x3. Find a unit vector x in R3 whose first…

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Q: Let C be a 6x6 matrix with. real eigenvalues -1, 2,4 and no complexores. Write the characterstic…

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Q: A real 2 x 2 non-singular matrix A w

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Q: Let Q(x) = 35x²7x27x3 + 18x1x2 + 18x1x3 − 18x2x3. Find a unit vector x in R³ whose first entry is…

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Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

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Q: If A is an n × n matrix with eigenvalue 0, then dim (null(A)) > 0.

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Q: Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -1 and…

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Q: Suppose A is a 2 x 2 real matrix with an eigenvalue λ = 1 + 4i and corresponding eigenvector -1 + i…

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