Linear Algebra - Elementary Row Operations

[squance]

Heys Im stuck on another problem. I would like some help please

Let Actually, there shouldn't be braces for that matrix..it should be one of those straight line brace things (to represent the determinant)

Find the following determinants:




The answer is 1. Can someone please help me work this out. (I can do similar questions with scalar multiples but with letters, Im not sure).

[/0]

Let the rows be [1], [2] and [3].
Subtract row [1] from [2] and place result in row [2]
Add twice row [1] to [3] and place result in row [3]
The matrix should look the same now as the first one now.

[squance]

Let the rows be [1], [2] and [3].
Subtract row [1] from [2] and place result in row [2]
Add twice row [1] to [3] and place result in row [3]
The matrix should look the same now as the first one now.

You forgot to add:
Add twice row [2] to [3] and place result in row [3] as the next augmented matrix

Anyways, I did follow that but I still don't get why the answer is 1.

Like for instance, determining the determinant of
 and if using the matrix I posted up in my first post, the answer would be 8 since each row is multiplied by 2 so, 2x2x2 = 8. Im basing this answer on a theorem that was printed on the lecture notes.

For question that required the answer 1, I think the relevant theorem is "If B is obtained from A by replacing a row (or column) of A by itself plus a multiple of another row(or column) then det(B) = det(A).

So based on that theorem, the answer to that matrix would be 1?

[phagist_]

It's 1 because those row operations do not affect the determinant.

There should be some rules listed in the lecture notes (if they are the same ones we used) on which elementary row operations affect the determinant and how they do so.

So the second matrix is obtained by;

Row 2 becomes Row 2 + Row 1
Row 3 becomes Row 3 - 2* Row 1

and adding or subtracting scalar multiples of rows should not affect the determinant (it should be stated in those rules in your lecture notes)

btw are you doing this as a summer course?

[squance]

Oh ok. Thanks heaps phagist_!!
Yeah I think the lecture notes are the same as for the people who did linear algebra last semester...except in this case, we have to fill in the gaps of the lecture notes by ourselves (I actually have many gaps that are not filled in because I have no clue and I can't ask anybody because no one that I know of has bothered to fill in their lecture notes...or start the purple question book for that matter)

Yes. Im doing linear algebra as a summer course.
I finish on the 16th of February and then the exam is on the 19th

Save me!

[brendan]

http://app.lms.unimelb.edu.au/bbcswebdav/courses/620156/HTML_S/STUDENTS/STUDENT_PDF_2009/156assign2.pdf

[squance]

Yes Brendan. I see the assignment. I'll start it later