Question

Hello,
In Unit 1:Vectors:Session 6: Determinants' notes. I can't understand the solution of example 1.1. Isn't evaluting the determinant should be 3*1 - (-2)*(-1) = 1? But in the answer it's 12 + (−8) + 1 − 6 − 8 − (−2) = −7 ?!

Answer 1

typo...

Answer 2

I think so. But in example 1.3 there is the same way of solution, but it's a correct answer - " A = −2 + 0 + 3 − 12 − 0 − (−1) = −10.
". Any ideas how it was solved this way?!

Answer 3

can you post the link

Answer 4

Here you are
http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-6-volumes-and-determinants-in-space/MIT18_02SC_MNotes_d1.pdf

Answer 5

the first example was a 2x2 matrix,
the second is a 3x3 matrix....
the methods for finding determinants in the two cases is slightly different

Answer 6

i think you are confused between example 1.1 and example 1.2

Answer 7

Yes, I know. But what I wonder about is the way of solving determinants, if you look at example 1.3, you'll find three ways, I just can't undstand the third solution. ( A= −2 + 0 + 3 − 12 − 0 − (−1) = −10 )

Answer 8

this is the essence of all the methods for a 3x3 matrix
1) choose any row (or coulmn)
2)multiply first element in that row with the determinant of the 2x2 matrix thats left after ignoring all the other elements of that respective row or coulmn,
repeat for second and third element of the row
3) add up all of them

Answer 9

the example shows the method first by choosing the first row and calculating the determinant, and then by choosing the second column and again calculating the determinant to show that the same answer is obtained

Answer 10

Exactly, and it also solves it by a another way just after solving it by the second column. that's what I can't undersatnd, but I really appreciate your helping.

Answer 11

the pdf solves by only two methods: 1st row and then 2nd coulmn

Answer 12

But what does this line mean - " Checking by (1), we have |A| = −2 + 0 + 3 − 12 − 0 − (−1) = −10 "?

Answer 13

i think the (1) is meant to refer to one of the direct formulas \(A_{11}a_{11}+....\)
but typos must have messed it up

Answer 14

Two typos messed up like this and in the same way is weird, but thanks for your help.

Answer 15

lol...it happens..
but other than the occasional typo, it is an excellent resource!!

Answer 16

That's for sure.

Answer 17

a helpful suggestion: the activity on this group is very little..
if you want quick help, post your questions on the "mathematics" group.( but you will have to provide links and more context) there are plenty of very smart users who love this stuff :)

Answer 18

OK, thanks a lot.

Answer 19

The question was answered here, thanks again.
http://openstudy.com/study?source=email#/updates/5691691ce4b0f78e197fa835