Does the following matrix have an inverse?


by frankR
Tags: inverse, matrix
frankR
frankR is offline
#1
Oct8-03, 07:55 PM
frankR's Avatar
P: 91
N= [i,1;-1,i]

I used this theorem: N N-1 = In

Thus:

[i,1;-1,i]*[a,b:c,d]=[1,1;1,1]

I then found:

ia+c=1
ib+d=1
-a+ic=1
-b+id=1

Can I conclude an inverse does not exist. If so, how?

If not, what do I do?


Thanks,

Frank
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
Hurkyl
Hurkyl is offline
#2
Oct8-03, 08:12 PM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,101
I2 = [1, 0; 0, 1]


What theorems have you learned about invertible matrices? (e.g. have you learned anything about how to tell if a matrix is invertible based on its determinant)


Or, you could apply the algorithm for computing inverses and see if you get an answer or if its impossible.
frankR
frankR is offline
#3
Oct8-03, 08:44 PM
frankR's Avatar
P: 91
Originally posted by Hurkyl


Or, you could apply the algorithm for computing inverses and see if you get an answer or if its impossible.
I just found this:

N-1 exists only if:

det(NN-1 != 0

I'm a little rusty on my linear algebra, plus I got a concusion yesterday.

arcnets
arcnets is offline
#4
Oct10-03, 06:17 PM
P: 513

Does the following matrix have an inverse?


frankR,
Hurkyl has told you what I2 is, because you got that wrong. Just redo your calculation using Hurkyl's hint and you should be able to answer this easily.


Register to reply

Related Discussions
Inverse Matrix General Math 14
Inverse of Matrix Sum Linear & Abstract Algebra 1
Inverse of a matrix Calculus & Beyond Homework 4
Inverse Matrix Linear & Abstract Algebra 7
Inverse matrix Calculus 3