The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+7 votes
425 views

What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$

  1. -1 and 1
  2. 1 and 6
  3. 2 and 5
  4. 4 and -1
asked in Linear Algebra by Veteran (18k points) | 425 views

2 Answers

+14 votes
Best answer

Let the eigen values be a,b

Sum of Eigen Values = Trace(Diagonal Sum)

 => a+b = 2+5 = 7

Product of Eigen Values = Det(A)  

 => a.b = 6

Solving these we  get 1 and 6.. So, Option(B) is Correct ..

answered by Veteran (17.5k points)
selected by
how did you derived this?
these are famous properties..
will this work as check for matrices of size grater than 2*2
always, for n*n matrices.
+3 votes
(2-x)(5-x)-4=0 x=1,6
answered by Veteran (14.3k points)


Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

33,687 questions
40,230 answers
114,268 comments
38,791 users