Question

Linear algebra,

can you please tell me why is this unique ?
https://www.dropbox.com/s/r5yrywzpe2igyx6/Screenshot%202013-11-15%2017.10.28.jpg


as far as I understand there can be a matrix with all elements zero or a matrix with all elements same as the other one but with different sign ? (hence not "unique" ) ?

Answer 1

suppose there are 2 such matrices...

\[O_1\text{ & } O_2\]

then\[A+O_1=A \text{ and }A+O_2=A \text{, right?}\]

But \[A-A=(A+O_1)-(A+O_2)=(A-A)+(O_1-O_2)=0\Rightarrow O_1-O_2=0\rightarrow O_1=O_2\]

Answer 2

\[\Rightarrow O_1=O_2\]

Answer 3

hm

Answer 4

so the unique one is the one with opposed signs

Answer 5

?

Answer 6

no, it's the zero matrix (m x n)

Answer 7

A+O=A => O is the zero matrix

Answer 8

does that make sense?