Question

Can someone help me out here. I am doing determinants and the question is saying that
ABC
DEF
GHI all equal 4

so given
def
abc
ghi

I am supposed to find the determinants!!????

Answer 1

This is a matrix I just don't know how to put matrix on the computer.

Answer 2

Do you mean
\[det\left(\begin{array}{ccc} A&B&C\\D&E&F\\G&H&I\\ \end{array}\right) = 4\]

Answer 3

yes

Answer 4

And you want to know
\[det\left(\begin{array}{ccc}D&E&F\\A&B&C\\G&H&I\\\end{array}\right) = ??\]

Answer 5

yes.

Answer 6

You multiply the original determinant by -1 for each row exchange.

Answer 7

so I multiply 4 by -1?

Answer 8

yep

Answer 9

so what happens when the next question
2a 2b 2c
d e f
g h i
do i then multiply 4 by 2 and then by -1? Does this make sense?

Answer 10

Just multiply 4 by 2. You don't have any row exchanges here (from the original matrix), so you don't need to multiply by -1.

Answer 11

if a row had of been changed i would of had to multiply 4by 2 and then by -1?

Answer 12

Yep

Answer 13

wow thanks

Answer 14

do you have to show your work for it?

Answer 15

do you have to show your work for it?

Answer 16

No, it's just using the properties of determinants. If anything you may want to write a sentence explaining why you are doing what you are doing so you don't have to learn it all over again later :)

Answer 17

If we interchange two rows, the determinant of the new matrix is -1 times the old one.

If we multiply one row with a constant, the determinant of the new matrix is the determinant of the old one multiplied by the constant,

Answer 18

what happens if it is multiplied by two different constants

Answer 19

you would have the original determinant times the first constant times the second constant.