Verify that ; is an eigenvalue of A and that x; is a corresponding eigenvector. A...
Verify that i; is an eigenvalue of A and that x; is a corresponding eigenvector. -1 4 -6 A = 4 5 -12 -2 - 4 3 11 = 13, X1 = (1, 2, -1) 12 = -3, X2 = (-2, 10) 13 = -3, X3 = (3, 0, 1) 1 AX1 5 -12 = 13 2 = 11X1 -1 Ax2 4 5 -12 -2 -4 3 22X2 -1 3 3 4 5 -6 - 12 Ах3 4 1: -3...
Verify that i; is an eigenvalue of A and that x; is a corresponding eigenvector. 5 -1 4 A = 0 3 1 21 = 5, X1 = (1, 0, 0) 12 = 3, X2 = (1, 2, 0) 13 = 4, X3 = (-3, 1, 1) 0 04 5 -1 4 1 1 Ax1 = 0 3 1 0 = 5 0 11 III = 11X1 0 04 0 0 5 -1 4 1 1 Ax2 0 3 1...
Verify that li is an eigenvalue of A and that x; is a corresponding eigenvector. A = -4 -2 37 -2 -7 5 1, [ 1 2 -6] 11 = -11, X1 = (1, 2, -1) 12 = -3, x2 = (-2, 10) 13 = -3, X3 = (3, 0, 1) [ 11 [ -4 -2 3 11 1] -2 -7 6 || 2 | 1 2 -6 1 -1 1] 2 Ax = = 21x1 [ -1 | [...
DETAILS LARLINALG87.1.006. Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 5 -1 2 an = 5, xn = 1, 0, 0) A =10 3 11; Ax = 3,x; = 1, 2, 0) 0 0 4 .[ (1 ,1 ,1-) = ;x,4 = ܨܬ 1 AX, ܐܐ 5 -1 2 0 3 1 0 0 4 ܐܐ ]. 0 ܕܫܢ AX, - 5 -1 2 0 3 1 0 0 4 2 =_32 ܕX,2...
A = A has a = 5 as an eigenvalue, with corresponding eigenvector and i = 8 as an eigenvalue, with corresponding eigenvector . Find the solution to the system * = }}yı – žy2 y = - 5471 + 34 y2 that satisfies the initial conditions yı(0) = 0 and y2(0) = 3. What is the value of yı(1)?
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. -4 A = X = 5 48-11
3 7. If A is a 3x3 matrix with eigenvector o corresponding to an 1-21 eigenvalue of 5 and 2 corresponding to an eigenvalue of 2, and v= 7 [10] 4 find Av. 6
Find (as a unit vector with negative first term) an eigenvector of the matrix corresponding to the eigenvalue lambda = 2 2 – 30 – 6 Find (as a unit vector with negative first term) an eigenvector of the matrix 0 2 0 corresponding to the eigenvalue 1 = 2 0 - 6 4 -4 1/3 x Preview Answer: 6V154 77 V154 154 3V154 154
Is A=3 an eigenvalue of A. If so, find one corresponding eigenvector. -1 0-2 2 5 - 4 0 2 -2 a. v=(-1,5,2) b. V=(1,5,1) c. V=(-5,6,1) d. X = 3 is not aneigenvlalue of A оа Ob ос