Solve Determinate Question Homework: 2x2 Matrix

[ElliottG]

Homework Statement

[URL]http://74.52.147.194/~devilthe/uploads/1318251620.png[/URL]

Homework Equations

None

The Attempt at a Solution

I asked my teacher the same question and she said this:

We didn't do an example like this in class, but you should be able to figure it out based on what we did do. You need to put a couple of things together:

1) What happens to the determinant of a matrix when you multiply one row by a scalar?

2) When you multiply a matrix by a scalar, what happens to it? (Answer: each entry gets multiplied by that scalar. But what does this mean for the rows?)

3) How many rows does this matrix have?

See if you can get it now!

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

 

[NascentOxygen]

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.

 

[SammyS]

...

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.
...

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

 

[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:

1) What happens to the determinant of a matrix when you multiply one row by a scalar?

 

[SammyS]

...

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:

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

 

[NascentOxygen]

Alright so I got it at 27.

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

 

[ElliottG]

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

Yup. What were you expecting then? :S

 

[HallsofIvy]

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:

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.

 

[NascentOxygen]

Yup. What were you expecting then? :S

I had in mind completing the answer as: det(-3A) = 9.det(A)
since it seemed you already had the answer partly filled in.

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

So 27 is good.

 

[HallsofIvy]

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

 

[NascentOxygen]

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

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!)

I answered it as: 9*det(A)
to accommodate that 9.

 

[SammyS]

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

 

[ElliottG]

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

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 into 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!