Please help me double check my answers for the practice problem. Pl

Exercise 5.2.1: Spanning sets and subspaces. Determine whether each statement is true given a subset S = b (a) S forms a subspace of R2 (b) The span of 3' forms a subspace of R2. Exercise 5.4> Finding the dimension of a subspace spanned by a set. Let S ={ 1], [3] . [8] . } and W = Span (S'). (a) Find a basis for W. (b) What is the dimension of W?Exercise 5.2.2: Determining whether a vector is in the span of a set of vectors. Determine whether each vector v is in the span of S. If so, write the v as a linear combination of vectors in S. a V (b V : (C 3 V = 3 (d) V =Exercise 5.2-4: Determining if a set spans a space. Determine whether each set spans the given vector space. ={= [hiW} Exercise 5.3.1: Linear independence and span. Determine whether the statement is true or false. Justify each answer or provide a counterexample when appropriate. (8) If a set is linearly dependent, then each vector in the set can be written as a scalar multiple of the other vectors. 0)) If a set contains fewer vectors than the number of components in each vector, then the set is linearly independent. (C) . I . I If a set contains one vector, then the set Is linearly Independent. (d) I I I I I if v1 and v2 are not scalar multiples and {V1, v2, V3} Is a linearly dependent set, then V3 Is In Span-[V1, v2}. (6) If {V1, v2, V3} is a linearly independent set, then Span{v1, v2} = Span{v1,v2,V3}. Exercise 5.3.2: Determining whether a set is linearly independent or dependent. Determine whether the given set is linearly independent or dependent. (a) (b) (c) (d) (e)Exercise 5.3.4: Finding a minimal spanning set. Find a minimal spanning set for the subspace spanned by the each set. (a (b ) 2 (c)Exercise 5.4.1: Basis and dimension. Determine whether the statement is true or talse. Justify each answer or provide a counterexample when appropriate. (3) If S is a linearly independent subset of a subspace H, then S is a basis tor H. (b) If S = {v1 , . . . ,vn} is a linearly independent set of vectors in R\Exercise 5.4.2: Determining whether a set is a basis. Determine whether each set is a basisfor IR* . If the set is not a basis, extend or reduce the set to a basis. (a) 5 8 (b) (c) (d)Exercise 5.4.7: Finding a basis for a subspace. Find a basis for each subspace. (a) W = X1 C1+2 =0} of R2 (b) W = AC 2 1 + 242 - 03 = 0 of R3