# Dividing a row/column of determinant

1. Apr 11, 2012

### Hernaner28

Hi. This is a property but I got confused with it when I thought about the quotient. Look at this:

$$\left| {\begin{array}{*{20}{c}} a&d&{2g}\\ {\frac{1}{3} \cdot 3b}&{\frac{1}{3} \cdot 3e}&{\frac{1}{3} \cdot 6h}\\ c&f&{2i} \end{array}} \right| = \frac{1}{3} \cdot \left| {\begin{array}{*{20}{c}} a&d&{2g}\\ b&e&{2h}\\ c&f&{2i} \end{array}} \right|$$

I need to transform that matrix into one a b c d e f g h i which I know its determinant is 5. But the teacher instead of taking out the 1/3 she multiplied 3! But doesn't say the property that if you multiply a row then you take out that number and multiply the determinant???
Thanks!

2. Apr 11, 2012

### Dick

You can pull the 1/3 out but that doesn't leave the matrix you've shown. What happened to the 3's?

3. Apr 11, 2012

### Hernaner28

If I have 6h and I multiply it by 1/3 then I get 2h.

4. Apr 12, 2012

### Dick

I don't get it. You can pull the 1/3 out leaving 6h in the matrix, or you can leave it in and have 2h in the matrix. You can't have both.

5. Apr 12, 2012

### Hernaner28

Oh yeah, now I realize. It's a colossal stupidity! Sorry for the trouble and thanks!