Mark each statement True or False. Please justify your answer?

a. Linearly independent set in a subspace H is a basis for H





b. If a finite set S of nonzero vectors spans a vector space V, then some subset of S is a basis for V.





c. A basis is a linearly independent set that is as large as possible.





d. The standard method for producing a spanning set for Nul A, described in Section 4.2, sometimes fails to produce a basis for Nul A.





e. If B is an echelon form of matrix A, then the pivot columns of B form a basis for Col A.








Please explain!Mark each statement True or False. Please justify your answer?
a) False, b) True, c) True, d) unknown...what is sec.4.2? , e) False.....Let the space be R^4 and let H be the subspace which students term R^3 .The set {[1,0,0,0],[0,1,0,0], } is L.I. in H but not a basis for H.... If S is not a basis for V then it is linearly dependent . So some of S can be discarded until the revised S is lin.ind., yet still spans V....This the definition of basis...a maximal linearly independent set in the vector space....let A have third row be a multiple of the first row. Then B has third row all zeros while the column space of A has nonzero entries in the third position