# Determinants of Variables

I am currently studying for a test, and I understand how to solve determinants when given concrete values. However, I have no idea how to solve this practice problem. Can someone lead me in the right direction to the solution?

Given

$det\begin{bmatrix}a & b & ... & c\\d & e & ... & f\\... & ... & ... & ...\\g & h & ... & i\end{bmatrix} = K$

Find the $det\begin{bmatrix}a & b & ... & c\\3d+a & 3e+b & ... & 3f+c\\... & ... & ... & ...\\g-d & h-e & ... & i-f\end{bmatrix}$

• Are the rows in the middle changed at all? – EuYu Oct 17 '12 at 2:12
• what is the size of the matrix? – ILoveMath Oct 17 '12 at 2:16
• The size isn't given. – Grace C Oct 17 '12 at 2:48
• I'm not sure about the rows in the middle. That's all that is given. – Grace C Oct 17 '12 at 2:48

1. Subtracting row $2$ from the last row
2. Multiplying row $2$ by $3$
3. Adding row $1$ to row $2$