Question

Session 6: Reading And Examples (Computing Determinants (PDF)).

Example 1-1: What is this equation in reference to? 12 + (-8).... is this an error in the course material? I notice it again referenced in equation 4). How is this equation derived? Thanks.

Answer 1

Can you scan and post the PDF file?

Answer 2

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 3

I am with you. Let me read more but so far, you are right

Answer 4

Interesting, thanks. I thought it was an error, but the same technique seems to be applied in Equation 4 as well.

Answer 5

yup, you are 100% right

Answer 6

Do you think it's the same error in equation 4 too, at the bottom?

Answer 7

nope, the Laplace expansion is correct.

Answer 8

the first one, they use row 1
the second expansion, they use COLUMN 2

Answer 9

And for the sign of entry, it will be
\[\left[\begin{matrix}+&-&+\\-&+&-\\+&-&+\end{matrix}\right]\]

Answer 10

hence for the first one, the numbers on Row 1 is +1, -0, +3
for the second one, when they use Column 2, the numbers and the signs will be
-0, +2,-1 as shown

Answer 11

of course, you have to multiple the cofactor matrices on each of numbers. I explained why and how they use the method.

Answer 12

I can see how the two end matrices are 2*(-7) -1*(-4) = 10, but the part under that where there is the equation.. |A| = −2 + 0 + 3 − 12 − 0 − (−1) = −10. How is that derived?

Answer 13

-10*

Answer 14

ok,
that is for second one, right?

Answer 15

Yeah, I assume so.

Answer 16

It says Checking By (1)?

Answer 17

\[2*\left|\begin{matrix}1&3\\2&-1\end{matrix}\right|=2*(1*(-1)-2*3)=2*(-7)\]

Answer 18

Correct

Answer 19

so??

Answer 20

Underneath that, the next sentence says something completely irrelevant? Checking by (1), and gives some weird equation also equalling -10, but the terms in it, I have no idea where they come from?

Answer 21

They might make mistake at the very first case on 2 x 2 matrix, but for the example 1-4, they are correct.

Answer 22

But do you see that sentence there in the PDF, which begins with "Checking by (1)"?

Answer 23

Because they assume that it is correct.

Answer 24

nope,

Answer 25

So that sentence is also incorrect there, the one appearing beneath equation 4 at the very bottom of the page?

Answer 26

(1) is correct, just only 1 line in example is not correct. Method (1) is CORRECT

Answer 27

In the attachment I've highlighted it

Answer 28

Is that circled red equation incorrect? I can't see how the -12 exists.

Answer 29

Can you post the previous PDF file? I want to see it. There might be something I didn't know. I would like to see the whole thing.

Answer 30

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 31

Give me more time, I will figure it out by checking from other site. I don't think they are wrong. MIT is an IVYleage school. They don't make that silly mistake, just our knowledge is not enough to understand.

Answer 32

Yeah, I could understand a typo in the first equation, but another at the end of example 1.3? Seems a bit much. Thanks I really appreciate your help.

Answer 33

It's late here so I'm going to go to bed, I'll accept your response But if you could post a reply with what you find out, I'd much appreciate it. Thanks again.

Answer 34

good night

Answer 35

****
I can see how the two end matrices are 2*(-7) -1*(-4) = 10, but the part under that where there is the equation.. |A| = −2 + 0 + 3 − 12 − 0 − (−1) = −10. How is that derived?
****

First, Example 1.1 is messed up. they present a 2x2 and show the work for a 3x3.

For Example 1.3, they are using the expansion shown in Example 1.4
(multiplying "diagonals" and "antidiagonals" )
one mnemonic is to "extend" the matrix, and find the product of the diagonals, like this