# Thread: Use properties of determinant

1. ## Use properties of determinant

The answer key says 8 but I'm getting 2. I think the problem is when I factor out the 1/2, should I be factoring out a 2 instead?

Any help is appreciated!

2. You made a very simple mistake.

You have $\displaystyle \det A = -4, -\frac{1}{2}\det B = -4$.

Therefore, $\displaystyle \det B = -4 \cdot -2 = 8$.

3. Originally Posted by icemanfan
You made a very simple mistake.

You have $\displaystyle \det A = -4, -\frac{1}{2}\det B = -4$.

Therefore, $\displaystyle \det B = -4 \cdot -2 = 8$.

I still don't understand, isn't there the property:

If B is the matrix that results when a single row or column of A is multiplied by a scalar k, then $\displaystyle det(B)= kdet(A)$

If I were to multiply det(A) by k=1/2 then I would get det(B)

So $\displaystyle det(B)= kdet(A)$

Or is it that I'm just thinking of this all backwards?

I know for sure that if (from another example) if I divided a row by some scalar k, say I divided by 2, I would have something like $\displaystyle kdet(A)$ so then $\displaystyle 2det(A)$

Thanks!

4. Originally Posted by DarK
I still don't understand, isn't there the property:

If B is the matrix that results when a single row or column of A is multiplied by a scalar k, then $\displaystyle det(B)= kdet(A)$
Precisely. The determinant of the matrix A before you multiplied one of the rows by 2 was 4. Hence the determinant of matrix B, which resulted from multiplying a row of A by 2, is 8.