

Solve the following system using the given eigenvalues. 2 2 3 X' 5 1 Х -3...
Solve the following system using the given eigenvalues. 2 2 -3 X' - 1 -5 X 3 4 4 0 = 1with multiplicity 3. Β Ι Ο e Paragraph
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
3. Homogeneous linear systems with complex and repeated eigenvalues. Find the general solu- tion of the given system of differential equations. For the two-dimensional systems, classify the origin in terms of stability and sketch the phase plane (a) x'(t) y'(t) 6х — у, 5х + 2y. = (b) 4 -5 x'(i) х. -4 (c) 1 -1 2 x'() -1 1 0x -1 0 1
3. Homogeneous linear systems with complex and repeated eigenvalues. Find the general solu- tion of the...
(1 point) Solve the system 2 1 dx dt х -5 -2 N with x(0) = 3 Give your solution in real form. X= X2 = An ellipse with clockwise orientation ✓ 1. Describe the trajectory.
0 2 0 Q1) Let A = 1 3 2 2 0 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue. Q2) Let aj, 02, 03, 04, agbe real numbers. Compute ai det 1 1 Q3) Determine all values of x E R such that matrix 4 0 3 х 2 5 A = is invertable. х 0 0 1 0 0 4 0
Question 3: Find the general solution of the system given as: -18 X'=13 Question 4: Find the eigenvectors and eigenvalues for the following system. 2 1 X's 2 6 5 2 Х Question 5: Solve the initial value problem. (State only the real part of solution) 8 - 2 1 XCO) - (3)
For the following exercises, solve a system using the inverse of a 3 x 3 matrix. 16.4x + 4y + 4z = 40 4 4 х 140 2x - 3y + 4z = -12 -3 4 y - x + 3y + 4z = 9 -1 3 4 2 -12 2 G
Given that A = 54 0 LO 3 -2 3 0] 0 has eigenvalues 11 = –2 and 12 = 4 and 4] 1 a basis for Exy is 1-2 %. 1] Choose ALL the statement(s) that are ALWAYS TRUE. = -2 are O A is NOT diagonalizable since the algebraic multiplicity and the geometric multiplicity of x different. A is NOT diagonalizable since the algebraic multiplicity and the geometric multiplicity of 12 = 4 are different. O A is...
6. Consider the following system x' = (^2 3)x. (a) Show that the eigenvalues are given by y + y2 - 16 2 (b) Give the interval(s) of y where the eigenvalues are real. (c) Give the interval(s) where the real eigenvalues give an asymptotically stable node. (d) Give the interval(s) where the real eigenvalues give an unstable node. (e) Give the interval(s) where the complex eigenvalues give an asymptotically stable spiral. (f) Give the interval(s) where the complex eigenvalues...
(1 point) Solve the system -3 -3 dx = х dt :: 1:) with x(0) = Give your solution in real form. Xi = X2 = An ellipse with counterclockwise orientation 1. Describe the trajectory.