I was reading determinants and there was this property of it:
If two parallel lines of a determinant are such that the elements of one line are equimultiples of the elements of the other line, then the value of the determinant is zero.
Please explain me what are equimultiples, I've read the article on Wikipedia but it didn't explain well according to me. Also give me an example of such determinant.
The entries in $(1,3)$ and $(10, 30)$ are equimultiples since you multiply by the same quantity, $10$, in each, to get the other.
In vector terms that's simply $$ (10,30) = 10(1,3). $$
The two vectors point in the same direction. One is a scalar multiple of the other.
This concept isn't about determinants, but it's useful when evaluating them. It tells you that the determinant of $$ \begin{bmatrix} 1 & 2 & 3 \\ 5 & 5 & 5 \\ 2 & 4 & 6 \end{bmatrix} $$is $0$ because the first and third rows are proportional (equimultiples).