Linear independence : Vectors $x_1, x_2,\ldots, x_n$ in a vector space are called linearly independent if $\lambda_1 x_1+\lambda_2x_2+\ldots+\lambda_nx_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$ In other words vectors are linearly independent if the only linear combination of the zero vector is the trivial one in which all coefficients are zero.