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Let A be a 2 × 2 matrix with eigenvalues −3 and −1 and corresponding eigenvectors v1 =
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- Find the eigenvalues and eigenvectors for the coefficient matrix.arrow_forwardFind the solutions of the system of linear equations if the eigenvalues of the matrix A arearrow_forwardSolve the following systems of equations using the matrix method. Find eigenvalues and eigenvectors by hand (but you can use technology to check your answers) (a) y' x + 2y = 2x + y " (b) x₁ = x₂ = 3x1 - 5x2 x1 + x2arrow_forward
- 4 Find all eigenvectors of the the matrix A = 2 3 (a) ; (b) ; (c) ; (d) ; C O b a d.arrow_forwardApply the eigenvalue method to solve the initial value problem:arrow_forwardConsider the Initial Value Problem: (a) Find the eigenvalues and eigenvectors for the coefficient matrix. X₁ (b) Solve the initial value problem. Give your solution in real form. 21 = x2 = v1 = I'₁ I'₂ = = -3x1 + 3x2 -6x₁ + 3x₂² x1(0) T2(0) = = 27 1810-181 and =arrow_forward
- Solve the following systems of equations using the matrix method. Find eigenvalues and eigenvectors by hand (but you can use technology to check your answers) (a) x' y' x + 2y 2x + y ' (b) x₁ 12 3x1 - 5x2 x1 + x2arrow_forwardFor #1(c), use diagonal factorization please.arrow_forwardplease type the answer instead of handwriting for better understanding thank you.arrow_forward
- Consider the Initial Value Problem: x₁ x2 X₁ = 0,₁ % v1 = 2x1 + 2x2 = = -4x12x₂² x1 (0) = 4 x2 (0) 6 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 181 = , and X₂ = ₁0₂ = (b) Solve the initial value problem. Give your solution in real form. x1 x2 = An ellipse with clockwise orientation phase plotter pplane9.m in MATLAB to describe the trajectory. [B] 1. Use thearrow_forwardx1 = x2 – 4x + 4x3 %3D 4 x½ = -3x2 - V3x, + V3x1 +X3 x3 = 7x2 - 2x1 Find the eigenvalues and eigenvectors by using the above equations.arrow_forwardyou are given the eigenvalues and eigenvectors for a 2 × 2 matrixA. Write down the general solution of dx/dt = Axarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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