Question

Suppose A = |a b c| it's a matrix
|d e f|
|g h i|
and det(A) = 6. Using only a simple calculator,
find det(M) where M = |a+d b+e c+f|
| g h i |
| d e f |

Answer 1

-6?

Answer 2

bingo ! ^_^

Answer 3

Thank you :D

Answer 4

but I have a question. why it's not changing when I add a row ?

Answer 5

basically, becasue adding a row doesnt change the outcome in a system of linear equations that the matrix models .... is what i think

Answer 6

well to get to that ans,,you need to study matrices deeply..i may not be even able to explain properly,,you should google over.

Answer 7

adding rows alters the way it looks, not the way it performs perhaps

Answer 8

why it doesn't change the outcome? talking about this matrix
det(M) = (a+d)(hf-ie) and so on....

Answer 9

in layman language,,since each term is exceeded by same no.,,on expansion,the extra no. gets cancelled out in the end..

Answer 10

you will get different answer if it's (a) itself not (a+d)

Answer 11

a+d is not a row operation

Answer 12

but it's not the same number in each one?

Answer 13

youre confusing your own concepts with the actual mechanics.

Answer 14

I'm trying to understand what you say

Answer 15

a matrix organizes information, its mechanics rely upon the nature of the material that it is organizing ... if tha tmakes any sense

Answer 16

yea it make sense for me

Answer 17

the math that is performed in a matrix resembles the math that is going on with the material that it is organizing, which makes it seem out of place

Answer 18

as far as determinants go, this might be useful in figuring that out:

http://www.es.ucsc.edu/~eart111/lecture12.pdf

Answer 19

Thanks @amistre64