Question

Linear algebra question... please see attachment.

Answer 1

Problem 3.5 part c.

Answer 2

what's the problem?

Answer 3

Did you see it in the attachment?

Answer 4

Yes. You're interested in the question that uses variables with numbers.

Answer 5

Yes

Answer 6

You treat it like you would a normal matrix

Answer 7

Ok so just to clarify, one column of this is not a scalar multiple of the other correct?

Answer 8

The part that I am running into problems with is where it tells me to use row operations to simplify calculations. To find the determinant I would need to make this matrix upper or lower triangular at minimum. Then I could multiply the diagonal and go backwards to find the determinant of the original matrix. The problem is that when I use row operations I get to a point where I can't eliminate anything else.

Answer 9

if you want the Det you can use the 3x3 shortcut

Answer 10

the det for that matrix is -6a^2b+6a^2c+6ab^2-6ac^2-6b^2c+6bc^2
not very pretty I know. :)

Answer 11

I can find the determinant by just using cofactors, or a multitude of other methods. I have to use the instructions in this problem.

Answer 12

It has to be using row operations to do so....

Answer 13

right.

Answer 14

Can you help me understand how to do it that way?

Answer 15

Cant you just get it into upper triangular form and just take the product of the diagonals?

Answer 16

I tried to do it that way but I am not able to get it into upper or lower triangular

Answer 17

However, that is what I am being asked to do.

Answer 18

Use row operations to eliminate the constants (3, 2, and 1). That leaves you with a column of two zeros and a constant. Then you can use cofactors to find the determinant, which will be simple since you only need to take the determinant of one 2x2 matrix.

Answer 19

Plug into the formula at the top of

https://en.wikipedia.org/wiki/Determinant

if you want

Answer 20

Ok that makes sense. I didn't think to do that. Would you agree though, that there is no way to calculate it by the diagonal? @DisplayError

Answer 21

I don't know if it's impossible, but it would definitely be a pain in the butt since you're dealing with three variables (you'd have to multiply the \(b\) row by \(c\) and the \(c\) row by \(b\), etc.) to try to get an upper or lower triangular form.

Answer 22

I am about to post one other question..... if you have a second could you take a look? It is the last one I have any confusion about.@DisplayError