My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 8th, 2013, 08:16 AM   #1
Newbie
 
Joined: Dec 2013

Posts: 2
Thanks: 0

Why Isn't This Matrix Invertible?

I need to show this matrix isn't invertible, but I'm not seeing why.

0 a 0 0 0
b 0 c 0 0
0 d 0 e 0
0 0 f 0 g
0 0 0 h 0
Magnesium is offline  
 
December 8th, 2013, 09:24 AM   #2
Senior Member
 
Joined: Jun 2013
From: London, England

Posts: 1,316
Thanks: 116

Re: Why Isn't This Matrix Invertible?

The middle row is a linear combination of the first and the last.
Pero is offline  
December 11th, 2013, 02:09 AM   #3
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Why Isn't This Matrix Invertible?

Another approach would be to show the determinant is zero. Expand along the top row.



Now we need to find that 4x4 determinant , expand along the second row.



Now that 3x3 determinant is 0 because it has a row of 0's , so det(A) = (-a)(e)(0) = 0

Therefore the matrix A is not invertible.

agentredlum is offline  
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
invertible, matrix



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
invertible matrix shine123 Linear Algebra 1 September 21st, 2012 08:47 AM
matrix invertible problem frankpupu Linear Algebra 3 March 6th, 2012 11:45 AM
Invertible matrix problem Linear Algebra 3 August 31st, 2011 05:30 AM
Find an invertible matrix P 450081592 Linear Algebra 1 June 24th, 2010 07:13 AM
AE=ED (Invertible and Diagonal Matrix) paulyc2010 Algebra 4 April 18th, 2010 02:50 PM





Copyright © 2019 My Math Forum. All rights reserved.