For each of the following matrices, find a fundamental matrix the system y' = Ay. Also say whether the trivial soln is unstable, asymptotically stable, or stable. 1 d) A =| 2 1 [-3 2 3.

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Q: T(x, y) = (-x, 4x + 8y, 9x − 3y, 6y – 5x). Find its associated matrix A. A = JUL

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Q: For each of the following matrices, find a fundamental matrix for the system y' = Ay. Also say…

A: We find the eigen value of given matrix A=-1-28-1 A-λI=-1-λ-28-1-λ=-1-λ-1-λ+16=1+λ+λ+λ2+16=λ2+2λ+17…

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: We have given  det(A) = 3 If B is singular matrix  det(B)  = 0 detBT=det(B) =0 So,  det2A-2BT =0…

Q: Find the Jacobi matrix for the following function. 5x + 6у f(x, y) = 5x - 4y? Jacobi matrix, (Df)(x,…

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Q: Given the tridiagonal matrix 1.1 0.198 0.83 1.8994 0.84 0.53 1.5044 0.2625 0.21 1.9541 ] work out…

A: Given tridiagonal matrix is A=1.10.198000.831.89940.84000.531.50440.2625000.211.9541 and its LU…

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Q: Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) x to find a solution…

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Q: Consider the planar system y' = Ay, where the matrix A has eigenvalues A = -2, X2 = -3. Where does…

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Q: Consider the following LU decomposition of the given matrix: 1 0 0 0T2 1 -1 2 2 1 -1 2 4 5 -3 6 0…

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Q: 3. Consider the homogeneous CLTI system i = Ax where 1 A -1 -1 1. a) Is A diagonalizable? If not,…

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Q: Give the value(s) of à for which the matrix A will be singular. -4 1 -2 A= 0 1 A 2 A={-2, 1} b)…

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Q: (d) Hence find a fundamental set of solutions r(1)(t), x(2)(t) and a fundamental matrix F(t) for the…

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Q: Consider the following nonhomogeneous linear system: xi = 3x1 + 4x2 + 10 cos t x2 = 3x1 + 2x2 %3D 2.…

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Q: Suppose that A is 2x2 matrix with eigenvectors V, which correspond to A, = 3, A2 = 2 respectively.…

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Q: 1.0 T(A) = 2AX - 2XA, where X is a fixednxn matrix %3D n,n mation ansformation

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Q: Find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A. 1 A = 2 1 Choose the…

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Q: Find a formula in terms of k for the entries of AK, where A is the Hermitian matrix below 13 4 9. 9.…

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Q: Find h and k, consistent: which makes matrix t. 6ud Sua = k |

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Q: Let O be a F.M. of the system Y-4Y on I, where A is 2x2 matrix. Then - [1 2 is also a F 1 3 a) True…

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Q: 4) Find the general solution of the following nonhomogeneous system: y' = [²¹] + [²], ÿ(0) = [-] e2t…

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Q: For a non-singular matrix A, A^(-1) is equal to: (adj(A)) / det(A) det(A) x (adj(A)) det(A) x A

A: Explained below

Q: Find a fundamental matrix of the following system, and then apply x(t)=(t)(0) 1x to find a solution…

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Q: Let +(t) = ( be a fundamental matrix of the homogeneous system 2 1 x'(t) = ( { 2 ) ×(). Which of the…

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Q: [1 0 2 31 l4 5 B = 6 ol,c = l6 ál, and V = |1|. What is the sum of the entries of the Lo. matrix VT…

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Q: Let O be a F.M. of the system Y'=AY on I, where A is 2×2 matrix. Then, . is also a 2 F.M. a) True b)…

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Q: DA. V = R"X", and S is the subset of all skew-symmetric matrices. OB. V = R"X", and S is the subset…

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Q: Consider a disease that propagates according to the system dx 357 — Зху — Зх dt - dy = x²y – 13xy –…

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