# Determinate question

1. Oct 9, 2011

### ElliottG

1. The problem statement, all variables and given/known data

2. Relevant equations
None

3. The attempt at a solution
I asked my teacher the same question and she said this:

Okay, so I know that when you multiple a row of a matrix by a scalar, the determinate also gets multiplied by that same scalar.

Know from the question that it's a 2x2 matrix we're dealing with.

Know that the determinate of a 2x2 matrix is ad-bc

I have no idea how to do this question it's the only one I can't get out of the whole assignment...

I still can't get it lol

Any help would be appreciated!

Thanks,
Elliott

Last edited by a moderator: Apr 26, 2017
2. Oct 9, 2011

### Staff: Mentor

Write down the 2x2 matrix whose determinate is ad - bc
Let's call this matrix A.
Write down matrix -3A
Determine the determinate of this matrix.
Compare with above.

3. Oct 9, 2011

### SammyS

Staff Emeritus
So, for -3 A, how many rows get multiplied by -3 ?

4. Oct 9, 2011

### ElliottG

Alright so I got it at 27. I did the matrix out like NascentOxygen said and it made more sense.

To answer your question SammyS, both rows get multiplied by -3 (now I see that).

I still don't see how this question is relevant to this problem, though:

5. Oct 9, 2011

### SammyS

Staff Emeritus
For each row of the matrix that you multiply by -3, multiply the corresponding determinant by -3.

6. Oct 10, 2011

### Staff: Mentor

27? I wasn't expecting that for the answer.

7. Oct 10, 2011

### ElliottG

Yup. What were you expecting then? :S

8. Oct 10, 2011

### HallsofIvy

Staff Emeritus
Both rows got multiplied by -3 so the entire determinant was multiplied by (-3)(-3)= 9. Since the original determinant was 3, the new determnant will be (3)(9)= 27 as you say you got.

9. Oct 10, 2011

### Staff: Mentor

I'd overlooked being told det(A) =3.

So 27 is good.

Last edited: Oct 10, 2011
10. Oct 10, 2011

### HallsofIvy

Staff Emeritus
??? Where did he say what his teacher's answer was?

11. Oct 10, 2011

### Staff: Mentor

I took it that teacher's answers are those in the boxes, and I looked at the one where he couldn't get the teachers answer. (Now seems unlikely!)

to accommodate that 9.

Last edited: Oct 10, 2011
12. Oct 10, 2011

### SammyS

Staff Emeritus
I think OP's answers are the ones in the boxes & the one boxed in red is wrong.

13. Oct 11, 2011

### ElliottG

Hahah sorry for the confusion but yes this guy hit it spot on.

Those are my answers in the box and I had already put an answer in to try it because it tells you whether you're right or wrong. I have unlimited tries.

Probably should have posted it without an answer in the box but you get the idea...

Thanks everyone!