Let x ? R3 be nonzero and let
A be the matrix whose columns are x,...
80.2K
Verified Solution
Link Copied!
Question
Basic Math
Let x ? R3 be nonzero and letA be the matrix whose columns are x, 2x,3x in this order. Show that x is an eigenvector of A andfind a basis for the null space of A.
Answer & Explanation
Solved by verified expert
4.4 Ratings (980 Votes)
Let x abcT where abc R and none of abc equals 0 so that x is not a zero vector Then A a 2a 3a b 2b 3b c 2c 3c The eigenvalues of A are solutions to the equation detAI3 0 or 3a22b23c2 0 or 2a2b3c 0
See Answer
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
