Question

How to prove vectors are linearly independent?

Answer 1

you can take the vectors to form a matrix and check its determinant. If the determinant is non zero, then the vectors are linearly independent. Otherwise, they are linearly dependent. and then change it to its row-echelon form,you can get the rank of this matrix

Answer 2

sum of the multiplication of the coefficient according to all there axis for both equation is zero.