Question

[Calculus:Vectors:determinants]

Hello,

In the following pdf there is a way of solving determinant I can't understand yet.

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

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.

Example 1.3, It's solved by 3 ways, I can't understand the 3rd way.

Answer 1

something looks fishy about that document - I agree for 1.1

Answer 2

The solution of 1.1 looks like it's from a 3x3 determinant, not a 2x2

Answer 3

My tip when dealing with determinants, find a method you're comfortable with, and stick with it, don't try to learn all possible ways of doing it, you're likely to confuse yourself or mix the methods. However if you're interested, I can explain how the third method is done, personally i prefer the third method.

Answer 4

Sorry, I mean't: don't try to attempt using all possible ways of solving a determinant. Learning about them is fine. Attempting to get the hang of all 3 at once is where it will snag you.