Solution is as follows
(1 point) -1 -4 a. Given that V1 [ 2] and U2 --10 are eigenvectors of the matrix _2] determine the corresponding eigenvalues. 4 11 = 12 = = -4x b. Find the solution to the linear system of differential equations x' y' satisfying the initial conditions x(0) = -3 and y(0) = 4. 4x – 2y x(t) = y(t) =
Question 19 (1-1 Find the eigenvalues and corresponding eigenvectors for the matrix 0 6 2 0-19 Selected Answer 21 = 8, x= (0,1,1) 12 = 7, x2 =(-1, 12,-6) d. hg = 1, 13 = (1,0,0)
Related to maths
Use Gaussian elimination method to evaluate the three currents. Question 2 The matrix A of the system AX = 2X is given by 10-1 A = 31 4 0 2 2 (a) Find the eigenvalues of A. (b) Determine the corresponding eigenvectors of A. in United States
F GHANA served) TEF RO HC 3 -2 0 A2. Given the matrix below 5 marks) [5 marks (10 marks (b) Compute explicitly the eigenvalues and determine the determinant, (c) Compute the corresponding eigenvectors of the matrix above (a) Show that the matrix is positive definite. 1 | so that the characteristic polynomial 5 marks 0 (d) Choose a, band c in the matrix B = | 0 Based on Cayley-Hamilton's theorem, every matrix fulfills its characteristic polynomial, using the...
Find the matrix A that has the given eigenvalues and
corresponding eigenvectors.
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
1 -1 1 Find the eigenvalues and corresponding eigenvectors for the matrix 0 6 2 0-19 Selected Answer: 21 = 8, x1 = (0,1,1) 12 = 7, 12 =(-1, 12, -6) d. 13 = 1, 13 = (1,0,0)
Please help me to solve these questions.
Exercise 4: Try to solve this questions! Using Matrix A, diagonalize the matrix by following the steps in (a) and (b). TO 0 0] A = 0 3 2 LO 0 1) a. Find the eigenvectors given by the corresponding eigenvalues, 2= 0, 1=1, q=3 (9 Marks) b. Construct matrix P from the eigenvectors and find the corresponding diagonal matrix, D given D = P-1AP (3 Marks)
Related to maths
In a given electrical network, the equations for the currents .., are given by +1 +11,0 21 - ₂ + 1 = 5.4 4+21,-1= 9.2 Use Gaussian elimination method to evaluate the three currents (10 mark Question 2 The matrix A of the system 1X = AX is given by 10 A=3 4 0 2 2 (a) Find the eigenvalues of A. (8 m (b) Determine the corresponding eigenvectors of A. (12 m 36 weet nhunted States
(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
4. Consider the following matrix [1 0 -27 A=000 L-2 0 4] (a) (3 points) Find the characteristic polynomial of A. (b) (4 points) Find the eigenvalues of A. Give the algebraic multiplicity of each eigenvalue (c) (8 points) Find the eigenvectors corresponding to the eigenvalues found in part (b). (d) (4 points) Give a diagonal matrix D and an invertible matrix P such that A = PDP-1 (e) (6 points) Compute P-and verify that A= PDP- (show your steps).