Q1. a. Find the eigen values of the following matrix and discuss the applications of eigen values in engineering disciplines. [25 4 A=0 6-3 00 8 b. Temperature of a disk brake plate at any point (x, y) varies is represented by the T(x,y)=100/(1+x³+y³ ) where T measure in °C and x, y in meters. Find the rate of change of temperature with respect to x direction and y direction and also the rate at a point (2,1).

Q: 5. From the eigenvectors of S = AAT/(n-1), find the line and the plane closest to the following…

A:

Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

A:

Q: x1(t) Let x(t) = be the solution to the discrete dynamical system: x2(t) x1(t + 1) = −8x1(t) +…

A: To solve this discrete dynamical system, we first find the eigenvalues and eigenvectors of the…

Q: Q.3. By using power method find the dominent eigenvalue and eigenvector for the following matrix. A…

A:

Q: Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix.…

A:

Q: a) Let A be the 2x2 matrix with eigenvalues 2 = 4,-1 such that E span E = span %3D Find both the…

A: Given:(a) A is  a 2×2 matrix with eigen value's λ=4,-1 and E4=span31 ,E-1=span12.  To find: Ak and…

Q: Find the eigen values of A = |K [2 -3. a) 1 = -3,4 b) 1 = ±V7 c) 1 = 2+ V3 d) 1 = 3, -4 3.

A:

Q: 1. (9pts) Diagonalize the matrix below by the following steps: 2 2 A: 1 3 -1 eigenvalues are λ = 5,…

A: Step 1: Step 2: Step 3: Step 4:

Q: Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow…

A: The phase plane is the graphical representation of all the solution curves of a system of…

Q: 7. For R, let A = Ag = cos sin sin 0 cos sin 0 and B Be= 86). cos cos sin (a) Show that B has an…

A: The rotation matrix in 2D is given.

Q: - find the eigenvectors of the diagonal matrix (Â) J where. 2 5 0-12 2 4 10 A = and P=["} 1 2 5 4 O…

A:

Q: The matrix T has eigenvalues and eigenvectors: with A,-1. with A=- with A- Sive formulas for the…

A: Note: According to our guideline, we will answer the first three subparts of the question as the…

Q: Consider the following system. dx dt Find the eigenvalues and eigenvectors. Number of eigenvectors:…

A:

Q: Let the eigenvalues and eigenvectors of matrix A4x4 be 21 = -5, v1 = d2 = 6, v2 = d34 = -3 + 2i,…

A:

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: Q.3) Consider the 2 x 2 matrix (3³) -6 A = Calculate all eigenvalues; Calculate all associated…

A:

Q: Find the matrix exponential The eigenvalues of A are X₁ = -1 and ₂ = 1. In the event that your…

A:

Q: tr(24+3) -(3) 8 Find the eigenvectors of matrix A

A: our objective is to find the eigen value.

Q: 2. Consider the following second-order ODE: * + 9x = 0. (a) Let y = x. Convert the above ODE into a…

A: The given differential equation is x¨+9x=0 and y=x˙ .

Q: 4. Find all eigenvectors of the matrix A = 1 %3D 1 (a) (b) (c) 6. 1 3 (d) (e) 1 1

A: Given :- to find Eigen vectors of the matrix A = 1411 To find Eigen vectors first we need to find…

Q: Q1 Find the eigenvalues and eigen functions for BVP yll + 2yl +(2+1)y = 0, y(0) = 0, y(5) = 0

A:

Q: {1+2i, 1– 2i, -3i

A: The solution is given as

Q: (3)= Cose +ising (9)

A: Eigenvector corresponding to an eigenvalue is NOT unique for a variety of reasons. Change the sign,…

Q: Find the matrix A of the quadratic form assoe 2x2 - 3xy - 2y2 + 11 = 0 A = Find the eigenvalues of…

A:

Q: From smallest to largest, the eigenvalues are X₁ < X₂ < A3 where A₁ = A₂ = Find the eigenvalues and…

A:

Q: For the system of differential equations, = A₁, A₂ = U₁ = U2 = y' a) Find the characteristic…

A:

Q: 5. Find a 3x3 symmetric matrix that has eigenvalues A₁ = 1, A₂ = 3, A3 = 5 and corresponding = (-¹).…

A: Given : λ1 =1 , λ2=3 , λ3=5          : K1=1-11  , K2=10-1  , K3=121 To Find : Symmetric Matrix

Q: -6 2 |X -3 0 2. Find the eigen value of the system: X' =

A: To find the eigenvalue of the system:

Q: + a. Find the eigenvalues of A matrix and the eigenvectors corresponding to these eigenvalues. 3…

A:

Q: 1. Given matrix A = [² ³1₁ 1/3 apply the power method to approximate (a) the eigenvalue with the…

A:

Q: Find all the eigenvalues and eigenvectors of the matrix 1 √2 2 √√2 3 √2 2 √√2 1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…