15. Given matrix N = Find the value of x such that NN' = 1, where I is -x the 2x2 identity matrix. (A) (C) (B) (D) 3/4

Q: B matrix= 3 X O oy Caluulate

A: The detailed solution is as follows below:

Q: part C D

A: Sol:- (a) First write the given system of differential equation in  x' = Ax form x' =-422-4xFor a…

Q: fu'(x)+v'(x)– 2u(x)– v(x) = 0 1-2u'(х) — v(х) + и(х) — 0

A: Let us consider the system of differential equation: X'=AX Where A is coefficient matrix of order…

Q: A 3 by 3 matrix is given below by B equals    {1  2  -1}    {1  0   1}    {4  -4  5} Find its…

A:

Q: 1. Find the numerical rank with tolerance 0.9 of the matrix 3 2 A = -4 -5

A: Answer

Q: 1.4: An eigenvector for value of λ = -2 for the matrix a) H b) [1] © H DE e) None of the above

A:

Q: Let x = [X₁ X2 X3]. Find the matrix A such that the system x' (t) = Ax(t) + f(t) is equivalent to…

A: Here is the solution of the given problem. Differential equation to system of differential equation.

Q: The 2 × 2 matrix A has a repeated eigenvalue 3. Moreover, we have (A – 31)v= w and (A – 31)w = 0…

A: In this question, we use the property of solution of the system of differential equation.

Q: Let A be an n x n matrix and let I be the n x n identity matrix. Show that if A? = I and A + I, then…

A:

Q: For which value of k does the matrix 3 k A 1 4 have one real eigenvalue of multiplicity 2? k = %3D

A:

Q: YQ12) Determine Eigen values and corresponding inverse of matrix for the following matrices: -1 1 -2…

A: Ans:-  We have to determine eigen values and      corresponding inverse of matrix.1  A=5-15020-53-15…

Q: 2 1 -1 4 previous problem to determine a matrix S such that Show that A is defective and use the 3…

A:

Q: 35.3. Consider a species in which both no individuals live to three years old and only one-year olds…

A: see the handwritten solution

Q: 17. Perform Gaussian Elimin ation on the matrix. [1 4 36 -1 -1 2 4. 0 4 -3-15 6,

A:

Q: Give general solutions for x,(t) and X2(t) dx, = x1 + 3x2 +1 dt dx2 = 3x1 + x2 +1 dt

A:

Q: 2. For the matrix (i) Find all eigenvalues, t.

A: Introduction: Let A be an n×n square matrix.If a NONZERO vector x∈Rn and a scalar fulfill Ax =λ x,…

Q: 26. If r3 +9x + 5 is divided by x, then remainder is 27. Find the value of x in the equation 2 log3…

A:

Q: 5. ( Consider the following linear system of differential equations: dY 2 3 Y. dt (a) Find the…

A:

Q: Writing x₁ = y and x₂ = dy/dr express the differential equation d²y + 2 d x+y=0 in the vector-matrix…

A: The problem is solved using the concept of eigenvalue and eigenvector.

Q: 50 Find the characteristic equation of the matrix 0 1 1 1 1 2

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Q: This is the first part of a two-part problem. Let P = -6 cos(6t) ý1(t) = - (sin(6t)) ] -6 sin(6t)…

A:

Q: Find the matrix exponential eAt for 1 2 A 0 3 By using eAt you have found in part (a), find the…

A: Consider the given matrix.

Q: Let the following system of differential equations be given. y′1=−8y1+4y2 y′2=−10y1+4y2 Write…

A:

Q: 1. Consier the following 4th-order linear differential equations dx dt4 + 10- + 35 dt2 + 50 + 24x =…

A: Given  equation is,…

Q: Q2A)Matrix 4 = [],find Eigen values of 1² A dy B)Solve differential equation=-(x²+y) dx x+siny

A:

Q: Consider the following system of nonhomogeneous first-order differential equations: (G :)** () ae X…

A: Particular solution of the system  X' = AX + b is: XP=Φ∫Φ−1b dt here Φ is fundamental matrix.

Q: Hence, write down the associated modal matrix P and diagonal spectrum matrix D, and use these to…

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Q: k1 has two distinct eigenvalues if and only if The matrix A = 1 9 k > Add Work > Next Question

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Q: 2. Find the general solution of the system of differential equations d 8 -5 х. dt 10 6 Hint: The…

A: The solution is given as follows

Q: 1. Solve the initial value problem by using the fundamental matrix (using other methods are not…

A:

Q: {1+2i, 1– 2i, -3i

A: The solution is given as

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: 3. Find the general solution of the system of differential equations 8 -5 di= 10 6 + 4t°e" ( cos(7t)…

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Q: educe from the result of Problem 31 that, for ev- y square matrix A, the matrix eA is nonsingular…

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Q: The initial value value problem - 5 -4 -1 X (0) =!, y co) interval With to be the is solved back…

A: The given matrix is  dxdtdydt=-5-432xy x'(t)=-5x-4y      ,         y'(t)=3x+2y x(t)=(-5x-4y)t   ,…

Q: 1. Consier the following 4th-order linear differential equations d4x + 10- dt3 d²x dx + 50 dt + 35 +…

A: Given differential equation is d4xdt4+10d3xdt3+35d2xdt2+50dxdt+24x=0             (i) Let us consider…

Q: 7 For the matrix H = 2: 41, find the 시, 2i] 2i 4 function H-1 using the diagonalization method (D…

A:

Q: 3. Suppose Un1= A U, is a matrix difference equation which describes discreet population changes…

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. Consier the following 4th-order linear differential equations d²x + 10- dt3 dx + 24x = 0 dt + 35…

A: (d) The fourth order differential equation: d4xdt4+10d3xdt3+35d3xdt3+50dxdt+24x=0 With initial…

Q: Consider the system of differential equations x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " where 1 and 2 are…

A:

Q: [1 1 t] 6.) Discuss how the rank of the matrix A = 1 t li 1 t-

A: first we can change in echelon form and then check how many non zero rows .

Q: Consider matrix K of order 3 defined by 3sene 3cose K = -3cose 3sene \3sene - 3cose 3sene + 3cose 3,…

A: To find the cofactor of the matrix

Q: find A-1 using Gaussian elimination and check the resul 3 -2 [1 1) A = |1 2 4. 27 1 1 Ans: A-1 = -2…

A: Explanation of the answer is as follows

Q: 1.4: An eigenvector for value of λ = -2 for the matrix a) H b) © H H e) None of the above is

A:

Q: In this problem you will solve the nonhomogeneous system 5 A. Write a fundamental matrix for the…

A: Here, Ψ-1=-sin3t34sin3t+3cos3t15cos3t33sin3t-4cos3t15g(t)=-14

Q: (2) Find the Hessian matrix Hf(x) of the given function and evaluate it at the indicated point. ㅠㅠ…

A: find the hessian matrix and evaluate at the point (a) fx,y=cosx siny , a=π4,π3

Q: x(0)-1 solve the initial value y(0)-0 problem with the matrix (eigenvector) method x'=x+y y' 4x-2y

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Q: Consider a system of differential equations which has the general solution: 18]- = C, · cos (5. t) –…

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Q: 1. E(Y,X, X2... X) (Y+Y2 +. + Yn) 2. E(IX,, X2, X) =E Y2+ + Yp) + -B(X, +X +

A: We have to show that β¯ is conditionally distributed.  To show β¯ conditionally distributed we will…

Q: Solve the following matrix system by using variation of parameters: dx *- ( )) 1 x + 5e-t %3D dt 4…

A: