## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

If these two equations are dependent, this means that they are the same equation, but one is multiplied by some constant $k$. Thus, when we find the determinant of the matrix, we will find: $$a_1b_2-b_1a_2$$ However, since the two equations are dependent, $a_1b_2\ and\ b_1a_2$ will be equal, so the expression above will evaluate to zero.