Redirected
in Linear Algebra
3,495 views
1 vote
1 vote
If the entries in each column of a square matrix M add up to 1, then an eigen value of M is

A) 4  B) 3  C) 2  D) 1
in Linear Algebra
3.5k views

2 Comments

Take identity matrix as an example where the condition " the entries in each column of a square matrix M add up to 1 " holds true. In such case eigen values are 1.

D)
3
3
Am getting 1 by taking examples.

Smallest example is order 1 matrix

$\begin {bmatrix} 1 \end{bmatrix}$

Eigen value is 1.
2
2

2 Answers

2 votes
2 votes
Consider the 2×2 matrix A=$\begin{bmatrix} a &b \\ c& d \end{bmatrix}$

$\lambda^2 -trace(A)  \lambda+det(A)=0$

$\lambda^2 -(a+d  )\lambda+(ad-bc)=0$

Put $\lambda$=1

$1-a-d+ad-(1-d)(1-a)=0$

$\text{as we know that a+c=1 and b+d=1}$

$1-a-d+ad-1+d+a-ad =0$

$0=0$ other option $\lambda=2,3,4$doesn't satisfy

$\mathbf{(D )ans}$

1 comment

i think after step 2 if u dont put the value of ƛ=1... u can enter into an equation where u can take (ƛ-1) common=0 which will give ƛ=1... ultimately answer.

0
0
1 vote
1 vote

 

Answer is 1 i.e. Option d . Here's the explanation :-

Related questions

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