Find a basis for the eigenspace of B below.-[₁02-35B=,λ = 2,3a.B={(1, 1), (2,3)}b.B = {(2,2),(1,1)}c. B={(2,3), (1, 1)}d.B={(4, 6),(-1,1))

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Answered: Find a basis for the eigenspace of B…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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
How do you get to the reduced form and then get the eigen vector in this problem?
3. If A = 0 -1 0then the bases for the eigenspaces of A2 + 21 are: 2. a) ({, = 7, v, = (1,0,0), {A2 = 4, v (-1,0,1)}, and (A = 1, v, = (-1,6,0}) b) {{ =-3, v, = (-1,6,0}), (A = 3, v (1,0,0}}, and (A = 0, v, = (1,0,0}] c) [{ = 27, v, = (1,0,0},{22 = 6, v = (-1,0,1}}, and (As = 3, s =(-1,6,0}} d) {{2 = 2, v, ={-1,0,1}}. [A2 = 23, , = [1,0,0), and (As =-1,, {-1,6,0}}
4.- From the following 3x3 matrix, obtain the characteristic polynomial, the eigenvalues and the eigenvectors. [-6 -3 -25] 1 2 A = 2 2 8 87 7
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
A matrix A E M(3, R) that has as eigenvalues 1, -1, -1 associated respectively to the eigenvectors (50, 50, -50), (0,16,16) and (24,0, -24) corresponds to?
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.
If A is a 3 x 3 matrix with Eigen values, x, y, z then the Eigen values of A'are 1 1 1 (a) y.z (b) -х, -у,-2 (с) (d) x. y.z

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Find a basis for the eigenspace of B below. 02 8-[-]₁1=2,3 ,λ = 2, 3 5 B= B=((1,1),(2,3)} B={(2,2), (1, 1)} C. B = {(2,3), (1, -1)} d. B={(4, 6),(-1,1)) a. b.