The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+13 votes
494 views
  1. Obtain the eigen values of the matrix

$$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$

asked in Linear Algebra by Veteran (59.5k points) | 494 views

3 Answers

+16 votes
Best answer
$5(a)$ the eigen value for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix
answered by Active (2.3k points)
edited by
0
we know for triangular/diagonal the determeinant is product of principal diagonal elements so in A-(lambda)I every value of lambda as any of of the principal diagonal elements will give result as 0. so all the diagonal principal diagonal elements are eigen values.
+6 votes
$A=\begin{bmatrix} 1& 2 &34 &49\\ 0& 2&43 &94\\ 0& 0 & -2&104\\ 0& 0& 0&-1 \end{bmatrix}$

$|A-\lambda I |=0$

$\begin{vmatrix} 1-\lambda& 2 &34 &49\\ 0& 2-\lambda&43 &94\\ 0& 0 & -2-\lambda&104\\ 0& 0& 0&-1-\lambda \end{vmatrix}=0$

$( 1-\lambda)( 2-\lambda)( -2-\lambda)(-1-\lambda)=0$

$\lambda=1\ ,\ -1\ ,\ 2 \ , \ -2$
answered by Boss (40.1k points)
+1 vote
Eigen value $lambda$=1,-1,2,-2 A-$lambda$I=0 just solve it and for the 2nd question i think building a truth table is a naive way of answering it if any1 has better solution then plz reply
answered by Boss (14.2k 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

37,118 questions
44,701 answers
127,278 comments
43,765 users