I will rate asap as the answer seems correct. Thx

Let V1, , v," E R" be vectors. We assume that span(vi, ,v,") = R". We call an index set I [L . . . , m} a basis, if the vectors {ie, are a basis of R". We assume that we are given cost c(1 ), . . . ,e(m) 0 for all the vectors and abbreviate c(I):-2ieic(i) as the cost of a basis. We say that a basis IC1,m) is optimal if c() c(I) for any basis 1 iii We want to compute an optimum basis and we want to use the following algorithm: (1Set -0 (2) Sort the vectors so that c(1) c(2) s... Sc(m) (3) FOR i1 TO m DO 4) If the vectorsi are linearly independent, then update 1-1) Prove that the computed basis / is optimal. Remark: Again, you might want to have a look into the correctness proof for Kruskal's algo rithm in order to solve this. Let V1, , v," E R" be vectors. We assume that span(vi, ,v,") = R". We call an index set I [L . . . , m} a basis, if the vectors {ie, are a basis of R". We assume that we are given cost c(1 ), . . . ,e(m) 0 for all the vectors and abbreviate c(I):-2ieic(i) as the cost of a basis. We say that a basis IC1,m) is optimal if c() c(I) for any basis 1 iii We want to compute an optimum basis and we want to use the following algorithm: (1Set -0 (2) Sort the vectors so that c(1) c(2) s... Sc(m) (3) FOR i1 TO m DO 4) If the vectorsi are linearly independent, then update 1-1) Prove that the computed basis / is optimal. Remark: Again, you might want to have a look into the correctness proof for Kruskal's algo rithm in order to solve this