If `vec(V_1),vec(V_2) ,.......................vec(V_n)` are vectors and `lambda _1,lambda_2,.......lambda_n` are scalar and if the linear combination
`lambda_1 vec(V_1) +lambda_2 vec(V_2) + ................+lambda_n vec(V_n) =0` , necessarily implies `lambda_1= lambda_2 = lambda_n =0` , we say that `vec(V_1),vec(V_2) ,.......................vec(V_n)` are said to constitutes a linearly independent set of vectors.
`text(Note: )`
`(i)` `2` non zero , non collinear vectors are linearly independent.
`(ii)` Three non zero , non coplanar vectors are linearly independent i.e. `[vec(a)vec(b)vec(c) ] ne 0 <=> vec(a),vec(b),vec(c)` are linearly
independent.
`(iii)` Four or more vectors in `3D` space are always linearly dependent.
If `vec(V_1),vec(V_2) ,.......................vec(V_n)` are vectors and `lambda _1,lambda_2,.......lambda_n` are scalar and if the linear combination
`lambda_1 vec(V_1) +lambda_2 vec(V_2) + ................+lambda_n vec(V_n) =0` , necessarily implies `lambda_1= lambda_2 = lambda_n =0` , we say that `vec(V_1),vec(V_2) ,.......................vec(V_n)` are said to constitutes a linearly independent set of vectors.
`text(Note: )`
`(i)` `2` non zero , non collinear vectors are linearly independent.
`(ii)` Three non zero , non coplanar vectors are linearly independent i.e. `[vec(a)vec(b)vec(c) ] ne 0 <=> vec(a),vec(b),vec(c)` are linearly
independent.
`(iii)` Four or more vectors in `3D` space are always linearly dependent.