Need help to find my mistake in a simple proof of a matrix algebra proposition.


by Brutus
Tags: algebra, matrix, mistake, proof, proposition, simple
Brutus
Brutus is offline
#1
Sep25-08, 01:20 PM
P: 7
1. The problem statement, all variables and given/known data
Is the following true for matrices?

Hypotesis:
AB = AC
A != 0(zero matrix)

Thesis:
B=C

3. The attempt at a solution

AB = AC
AB - AC = 0(zero matrix)
AB - AC = A(B-C) // using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices
A(B-C) = 0 <=> B=C because A != 0
QED

There is something wrong because there are matrices where AB = AC and B != C.
Where is my mistake?
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
Dick
Dick is offline
#2
Sep25-08, 01:32 PM
Sci Advisor
HW Helper
Thanks
P: 25,165
There are matrices where AB=0 and neither A nor B are zero. You can't say A(B-C)=0 implies A=0 or (B-C)=0 like you can with real numbers.
Brutus
Brutus is offline
#3
Sep25-08, 01:45 PM
P: 7
ok, thanks


Register to reply

Related Discussions
Linear algebra, prove matrix inverse proof flawed Calculus & Beyond Homework 9
Simple Matrix algebra Advanced Physics Homework 5
Simple matrix algebra Advanced Physics Homework 6
lin algebra: find the matrix with respect to basis... Calculus & Beyond Homework 6
Proof in simple Algebra Introductory Physics Homework 2