 In order to determine if the three vectors in R4,
are linearly dependent, form the matrix equation,

Row reduce this equation to obtain,
Rearrange to solve for v3 and obtain,
This equation is easily solved to define non-zero "a"i,

where "a"3 can be chosen arbitrarily.Thus, the vectors "v"1, "v"2 and "v"3 are linearly dependent.An alternative method relies on the fact that "n" vectors in formula_29 are linearly independent if and only if the determinant of the matrix formed by taking the vectors as its columns is non-zero.