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Differential Equations and Linear Algebra (4th Edition)
- 2.arrow_forwardConsider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = i *-[33]; -5 -3 .7₁ -3-1 5 b. Find the real-valued solution to the initial value problem y = {{ 3y + 2y₂, -5y₁ - 3y2, and A₂ = -1. Usef as the independent variable in your answers. y₁ (t)= -8cos(t)0-15sin(t) y2 (t)= -8cos(t)+15sin(t) y₁ (0) = -8, 32 (0) = 15. -3+i 5arrow_forwarddo a b c onlyarrow_forward
- Find the triangular factorization A = LU for the matrix 2 4 -6 A= 1 5 3 1 3 2 and solve LY = B, UX = Y , and verify that B = AX for B = [−4 10 5]T.arrow_forwardq14. true or false ?arrow_forwardGiven matrix A and its first two eigenpairs: A = 2 2 a b c6d e f -4 - 1 Lax-[A] λ₁ = 3, X₁ 2₂=-3, X₂= ¡ 1. 2. 3. 4. Complete the elements of Matrix A. Solve for p(2) = det(A-2) Find the third eigenpair of Matrix A. What is the algebraic multiplicity M and geometric multiplicity m and defect ^ ?arrow_forward
- whit the steparrow_forwardFind formulas for the voltages x, and x2 (as functions of time t) for the following circuit represented by the 2x2 matrix A. Assume R₁ = 1/5 ohms, R₂ = 1/3 ohms, C₁ = 4 farads, C₂ = 3 farads, and an initial charge of 4 volts on both capacitors. X(t) = X₁ (1) X2 (1) A X₁ (1) X₂ (1) given A= Click the icon to view the circuit. (1/R₁+1/R₂) C₁ R₂C₂ R₂C₁ -1 R₂C₂arrow_forwardFor each of the following systems of differential equations, use the eigenvalues and eigenvectors of the coefficient matrix to find the general solution. A. B. *1-2x17x2 2x14x2 = *1 = 2x1 *2 = 5x2 - 7x3 *3 = 2x₂ - 4x3arrow_forward
- Solve for p(λ) = det(A−λI).arrow_forwardShow the complete solutionarrow_forwarda. Determine the solutions of the simultaneous equations given below y = x² + x + 1 y = 6x + 7 b. Solve the following inequality: |3x + 1| <3 c. Solve the following equation using logarithm, correct to 3 significant figures. 33t-1 = 7t+1 3 d. Simplify the matrix multiplication 2 -1 -4 7 31 e. Find the inverse matrix of Matrix A = =[-_-2-3] 6 5 f. Find the determinant of the Matrix B= 2 -2 -4 NÁG 5 2 -2 ܢܐ ܗ ܚ 6 -3 1 0 3 -3 X م بل ه -3 0arrow_forward
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