Determinants homework question

[morbello]

determinants and the positive and negetive parts off the equation.

ive had a couple say they change when they are worked out.

on a second order process off mulitiplying diagonally

1 (-1 -11) - -3(1 -11) + -3(2 -1)
(1 5) (3 5) (3 1 )

they are joined together and matrics above


1(-5+11) +3(10 +33)-3(2+3)
= 6+3(43)-3(5)
=6+129-15=135-15=120

ANs 120

+\ mulitiply -1*5 and the -/ mulitpy1*11 making the 1(-5+11) would it not be 1-(5 -11) as the rule imforms you.

 

[HallsofIvy]

determinants and the positive and negetive parts off the equation.

ive had a couple say they change when they are worked out.

on a second order process off mulitiplying diagonally

1 (-1 -11) - -3(1 -11) + -3(2 -1)
(1 5) (3 5) (3 1 )

they are joined together and matrics above

It's very difficult to figure out what you are trying to say here.
I think you mean that you want to find the determinant
$$\left|\begin{array}{ccc}1 & -3 & -3\\2 & -1 & -11\\3 & 1 & 5\end{array}\right|$$
(that "1" in "(1 -11)" is a typo, isn't it?)

1(-5+11) +3(10 +33)-3(2+3)
= 6+3(43)-3(5)
=6+129-15=135-15=120

ANs 120

Yes, that is correct.

+\ mulitiply -1*5 and the -/ mulitpy1*11 making the 1(-5+11) would it not be 1-(5 -11) as the rule imforms you.

What rule? 1(-5+ 11)= (-1)(5- 11) since 1(6)= (-1)(-6) but 1-(5-11) means 1 subtract 11 which is certainly wrong.

 

[morbello]

in the matrics

-1 *5 is a positve multiplication and 1 *-11 is a negitive mulitiplication across the matric would this not effect the answer in the bracets or would allways be 1(-5+11)

im still trying to work out how to write up on here the brackets for a matice but thank you for your help.

 

[HallsofIvy]

I don't understand what you mean by a "positive multiplication" or a "negative multiplilcation". a(b+ c)= ab+ bc no matter what a, b, and c are.

 

[morbello]

in the book I am studying it has a diagonal mulityplication system ie were 1 and -11 are the top row and 1 and 5 are the bottom row.

so top right is mulitiplyed with bottom left. do you see what i mean and what i wanted to know was there a main reason that or what made the addition or subtraction as a result off the mulitiply in the 1(-5+11)

 

[NoMoreExams]

morbello: I would recommend reading either of these:

http://en.wikipedia.org/wiki/Determinant#3-by-3_matrices
http://en.wikipedia.org/wiki/Rule_of_Sarrus