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-2 2 A = 2 2 -2 4 Step 3: Find a possible basis for the smaller eigenvalue X1. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the smaller eigenvalue A1 is a d where a= 1 . b= 1 , c= 1 ,d= 1 are all positive integers with no common divisor.

-2 2 A = 2 2 -2 4 Step 3: Find a possible basis for the smaller eigenvalue X1. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the smaller eigenvalue A1 is a d where a= 1 . b= 1 , c= 1 ,d= 1 are all positive integers with no common divisor.

Advanced Engineering Mathematics
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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Lambda 1 = 2 

Lambda 2 = 4

Please explain how to get the basis for each of them

-2 2 A = 2 2 -2 4 Step 3: Find a possible basis for the smaller eigenvalue X1. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the smaller eigenvalue A1 is a d where a= 1 . b= 1 , c= 1 ,d= 1 are all positive integers with no common divisor.
Transcribed Image Text:-2 2 A = 2 2 -2 4 Step 3: Find a possible basis for the smaller eigenvalue X1. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the smaller eigenvalue A1 is a d where a= 1 . b= 1 , c= 1 ,d= 1 are all positive integers with no common divisor.
[ 4 -2 2 A = 2 2 -2 4 Step 4: Find a possible basis for the larger eigenvalue A2. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the larger eigenvalue A, is {E} where a= 1 and b= 1
Transcribed Image Text:[ 4 -2 2 A = 2 2 -2 4 Step 4: Find a possible basis for the larger eigenvalue A2. There are infinitely many possibilities but we will restrict ourselves to fill in only either 1 or 0. Answer: a basis for the eigenspace corresponding to the larger eigenvalue A, is {E} where a= 1 and b= 1
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