Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector.11 = 9, x, = (1, 0, 0)| 12 = 7, x2 = (1, 2, 0)0 8] 13 = 8, x3 = (-1, 1, 1)9 -1 2A =7 19 -1 211Ax1 :7 1= 9 00 89 -1 211Ax, =7 12= 7 20 89 -1 2-1-1Ax3 :7 1= 81=13x31%3D0 811

We have to verify that λi is an eigenvalue of A and that xi is a corresponding eigenvector.

Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 9 -1 2 2, = 9, x, = (1, 0, 0) A = 7 1 1 12 = 7, x2 = (1, 2, 0) %3D 0 8 Лз 3D 8, х3 %3D (-1, 1, 1) 9 -1 2 7 1 1 Ax, = = 9 0 = 1,x1 0 8 9 -1 2 1 1 Ax2 = 7 1 2 = 7 2 = 12X2 %3D %3D 0 8 9 -1 2 1 Ax3 = 7 1 = 8 1= 13x3 %3D 0 8 1 1

Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 9 -1 2 2, = 9, x, = (1, 0, 0) A = 7 1 1 12 = 7, x2 = (1, 2, 0) %3D 0 8 Лз 3D 8, х3 %3D (-1, 1, 1) 9 -1 2 7 1 1 Ax, = = 9 0 = 1,x1 0 8 9 -1 2 1 1 Ax2 = 7 1 2 = 7 2 = 12X2 %3D %3D 0 8 9 -1 2 1 Ax3 = 7 1 = 8 1= 13x3 %3D 0 8 1 1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

Verify that 1, is an eigenvalue of A and that x, is a corresponding eigenvector. 21 = 5, x, = (1, 2, –1) 12 = -3, x, = (-2, 1 0) d3= -3, x, = (3, 0, 1) -2 2 -3 A = 2. 1 -6 -1 -2 -2 2 -3 1 AX 1 2 1 -6 5. = 1,×1 -1 -2 -2 2 -3 Ax2 = 1 -6 = 12X2 2. -1 -2 -2 2 -3 3. -3 Ax3 21 1-6 0. %3D -1 -2
1(1)
Q6
Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. 3 0 A = [ A₁ = 3, x₁ = (1, 0) 2₂ = -3, x₂ = (0, 1) 0 -3 AX1 ~-[D-F= -0) --- 3 = 0 -3 3 *-*«DE÷-0→ AX2 = = = ไป = 22x2 ↓ 1
Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. 2₁9, x₁ (1, 0) = - [8. AX1 = AX2 A = = 9 0 0-9 = 22-9, x₂ = (0, 1) = = ↓ 1 = 9 0 -9 22x2 ~-(:D)- E= -0)-*-*2 1 0-9 ↓1 •[:] · = 2₁x1
Verify that A is an eigenvalue of A and that x, is a corresponding eigenvector. 4 -2 = -11, x; = (1, 2, –1) 22 = -3, x, = (-2, 1 0) 23 = -3, x; = (3, 0, 1) A = 2 -7 6 2 4 -2 13 Ax- 2 -7 6. 2 -11 2 !! 2 4 -2 2 AX2 -2 -7 !! %3D !! 4 -2 AX3 2 -7 = 13x3 1
Verify that λi is an eigenvalue of A and that xi is a corresponding eigenvector.
Matrix A has the eigenvalue 2 = 5 and eigenvector v. Find generalized eigenvector. 7 1 01 1|,λ5, ν = A = -3 4 -2 1 41 X2=