Let A || 9 3 -13 -4 0 0 -5 (a) Find the characteristic polynomial of A. (b) Find the two eigenvalues of A. (c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.

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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Let
A =
3
-4
-13
0
-5
(a) Find the characteristic polynomial of A.
(b) Find the two eigenvalues of A.
(c) Find a basis for the eigenspace corresponding to the smallest eigenvalue.
(d) Find a basis for the eigenspace corresponding to the largest eigenvalue.
Transcribed Image Text:Let A = 3 -4 -13 0 -5 (a) Find the characteristic polynomial of A. (b) Find the two eigenvalues of A. (c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.
(A) {(-2,0,1)} (B) {(-3,0,1)} (C) {(1,0,1)} (D) {(-4,0,1)} (E) {(0,0,1)} (F) {(-1,0,1)} (G) {(2,0,1)}
(H) {(3,0,1))
(c): Select
(A) {(13,0,1)} (B) {(15,0,1)} (C) {(16,0,1)} (D) {(17,0,1)} (E) {(12,0,1)} (F) {(14,0,1)} (G) {(18,0,1)}
(H) {(11,0,1)}
(d): Select ✓
Transcribed Image Text:(A) {(-2,0,1)} (B) {(-3,0,1)} (C) {(1,0,1)} (D) {(-4,0,1)} (E) {(0,0,1)} (F) {(-1,0,1)} (G) {(2,0,1)} (H) {(3,0,1)) (c): Select (A) {(13,0,1)} (B) {(15,0,1)} (C) {(16,0,1)} (D) {(17,0,1)} (E) {(12,0,1)} (F) {(14,0,1)} (G) {(18,0,1)} (H) {(11,0,1)} (d): Select ✓
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