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okay and this video I want to talk about

finding the determinant of a 3x3 matrix

so here's gonna be my matrix a and again

the entries are a sub 1 1 1 2 1 3 2 1 2

2 2 3 3 1 3 2 3 3 I'm kind of just again

a generic way of writing a matrix and

the notation is you know for the

determinate of a you either write Det of

a or they put it looks like absolute

value and it says to compute the

determinant of a 3x3 matrix basically

what you do is if you look at stuff

along the top okay so I'm gonna look at

my a 1 1 basically the formula is you

take that term a11 and I imagine kind of

a kind of cancelling out that row or

excuse me that column and that row I

think what am I left with I'm left with

a smaller matrix a.22 a23 a32 a33 okay

so I've got to take this coefficient a11

times this smaller determinant and

remember to calculate a smaller

determinant you multiply the diagonals

and then subtract the product of the

other kind of diagonal so I assume if

you if you're looking at a 3 by 3 matrix

you know how to do a 2 by 2 but we'll

talk about this in a second as well just

in case so now we do the kind of the

same thing we look at the same same row

but we move over ok we look at that guy

it turns out that there ends up you have

to change the sign so it's going to be a

sub 1 2 and again I think if I were to

cover up that column and that row the

stuff that I would be left with would be

that a 2 1 a 2 3 the a sub 3 1 and the a

sub 3 3

okay looks like I'm running out of room

here and then we go to the last one as

well so okay so the same thing I look at

the a sub 1 3

I imagine covering up that row and that

column and I'm left with the smaller

determinant to compute a 2 1 a 2 2 a 3 1

and a 3 2 okay so this is kind of the

the basic formula for computing a 3 by 3

determinant so pretty tedious but let's

see if we can't can't do one here so

let's let's come up with some specific

numbers I don't know I'm just going to

make up a matrix at random hopefully the

numbers won't be too terrible so I don't

know how about 1 6 4 I'm gonna keep

everything positive just hopefully to

keep keep it keep it straightforward one

six four two seven three eight nine what

are we missing five about five okay so

let's compute the determinant of this

matrix so again it says the determinant

the Det of that matrix a it says again

we look at the the first value which is

a 1 and again if I were to cover up that

row and column column in row

I've got to compute the smaller the

determinant of the smaller matrix 7 3 9

5 again it says we put a minus sign in

the middle ok if I look at the next

entry it's gonna be a 6 so that's what

I'm gonna put in there next and again if

I cover up that column with the 6 and

that row what am I left with it looks

like I'm gonna be left with the 2

the 3 the 8 and the 5 and then to that I

have to add on ok so now we just move

over my next value will be a 4 so if I

cover up that column and that row I'm

gonna have 2 7 8 9 left over okay so

that's kind of the set up so now all we

have to do is compute the individual

determinants so remember to compute a

determinant of a 2 by 2 matrix we

multiply the top left and the bottom

right so we'll get 7 times 5 we put a

minus sign in between there and then we

multiply the other diagonals so 3 times

9 then we'll get minus 6 we'll have to

take 2 times 5 minus 3 times 8 and then

plus 4 we'll have to take 2 times 9

minus 8 times 7 okay so now we're almost

there it's just a little bit of

computation at this point so we get 1

times let's see it looks like we get 35

minus 27 so 35 minus 27 let's go ahead

and write it out minus 6 2 times 5 is 10

minus 24 plus 4 times 2 times 9 is 18

minus 56 so 35 minus 27 is going to be 8

times 110 times

excuse me 10 minus 24 will be negative

14 so we'll get negative 6 times

negative 14 let's see so 18 minus 56

what is that negative looks like 38 to

me

so if we simplify this we'll get eight

two negatives make it positive let's see

what is that 84 six times 14 should be

84 and then we'll get a negative four

times 38 so what's that one 52 it looks

like okay you can check my arithmetic

here hopefully I'm not doing any crazy

arithmetic so eight plus 84 that's gonna

give us 92 minus 152 so the determinant

of this would be negative 60 okay

assuming all my arithmetic is correct

so again I think the main thing you know

it's just knowing the setup again just

take the first row first column and then

again you're just basically breaking it

down to smaller determinants again make

sure that you notice that the again the

signs are positive its negative and then

positive it's easy to leave out I think

that minus sign and then things don't

quite work out so all right I hope this

video makes some sense and helps out

feel free to post comments and questions

if you have them hopefully me or

somebody else can point you in the right

direction