Question:
Linear combination of the given vectors
Suppose {v_1, v_2, v_3} is linearly independent set of vectors in R^n. Determine which of the following sets of vectors are linearly independent and which are linearly dependent. If a set is linearly dependent give, a linear dependence relation. (Use the following technique. If {w_1, w_2, w_3} denotes one of the sets below, solve the equation c_1w_1 + c_2w_2 + c_3w_3 =0 for (c_1, c_2, c_3)
(a) {2v_1, 3v_2, -5v_3},
(b) {v_1 +v_2, v_1 - v_2, v_3}
(c) {v_1 + v_2, v_1+v_3, v_2-v_3}