Register to reply

Linear Algebra: Determinant

by drosales
Tags: algebra, determinant, linear
Share this thread:
drosales
#1
Feb21-12, 10:18 AM
P: 9
I need help with another homework problem

Let n be a positive integer and An*n a matrix such that det(A+B)=det(B) for all Bn*n. Show that A=0

Hint: prove property continues to hold if A is modified by any finite number of row or column elementary operations

It seems obvious that A=0 but i'm having trouble developing the proof. Any help would be great.
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
micromass
#2
Feb21-12, 10:36 AM
Mentor
micromass's Avatar
P: 18,346
Please post homework in the homework forum. I moved it for you now.

A hint for the proof: can you write a row/column operation as an elementary matrix??
drosales
#3
Feb21-12, 11:03 AM
P: 9
Yes and the product of the elementary matrices returns
A=E1*E2*..*En

is this what you are referring to?

micromass
#4
Feb21-12, 11:05 AM
Mentor
micromass's Avatar
P: 18,346
Linear Algebra: Determinant

Yes. Let E be an elementary matrix, can you show that

[tex]det(EA+B)=det(B)[/tex]

??
drosales
#5
Feb21-12, 11:49 AM
P: 9
Im not quite sure how to show this
micromass
#6
Feb21-12, 12:13 PM
Mentor
micromass's Avatar
P: 18,346
Hint: [itex]B=EE^{-1}B[/itex].

Use that [itex]det(XY)=det(X)det(Y)[/itex].


Register to reply

Related Discussions
Linear Algebra: Determinant Calculus & Beyond Homework 7
Linear algebra determinant Introductory Physics Homework 4
Linear algebra determinant Precalculus Mathematics Homework 12
Linear algebra: Determinant Calculus & Beyond Homework 1
Linear algebra determinant of linear operator Calculus & Beyond Homework 1