Let A = {v1, v2, v3, v4, v5} where each vi is independent. Is {(v2 - v3 ), (v1 + 2 v2 ), (v1 + v2 + v3 ), v4 , v5} linearly dependent or independent? Hint: Assume that there are five coefficients: a, b, c, d, e, for which: a (v2 - v3 ) + b (v1 + 2 v2 ) + c (v1 + v2 + v3) + d (v4) + e (v5) = 0 This means, the vectors are independent iff a=b=c=d=e=0. Thus, rearrange the above equation: v1(b+c) + v2(a+2b+c) + v3(-a+c) + v4d + v5e = 0 It means for independent system, a+2b+c = 0, -a+c = 0, b+c = 0, d = 0, e = 0. Use Gaussian-Jordan elimination to find if all the coefficients are 0 using the above 5 equations.