How to determine column dependency without calculating the determinant?

Determine whether this matrix' columns are linearly dependent or not.

$$\begin{bmatrix} 1 & 0 & 2 \\ 0 & -1 & -2 \\ 2 & -2 & 0 \end{bmatrix}$$

The determinant is $0$ - therefore they are linearly dependent!

Without making any calculations.

Whoa there. How do you determine column dependency without calculating the determinant?

• Add the first two columns. – user61527 Apr 9 '14 at 5:03

Write a linear combination of column 1 and 2, that is $2C_1 + 2 C_2$.
• You mean a combination of the form $aC_1 + bC_2 = C_3$? – Zol Tun Kul Apr 9 '14 at 5:06