At least one of the answers above is NOT correct (1 point) Are the following sta

Question

At least one of the answers above is NOT correct (1 point) Are the following statements true or false? True . I Si is of dimension 3 and is a subspace of R, then there can not exist a subspaceS2 of R' such that Si C S R with Si S and False-) 2. Rn has exacty one subspace of dimension m for each of m-0, 1, 2, . . . , n True True 4. The set (0) forms a basis for the zero subspace. False vl 5. The nullity of a matrix A is the same as the dimension of the subspace spanned be the columns of A 3. Let m > n. Then U ={ui,u2, ,Um} in Rn can form a basis fr R. if the cored m _ n vectors are removed torn U. Note: In order to get credit for this problem all answers must be correct

Explanation / Answer

The statement is False. We know that a standard basis for R4 is {(1,0,0,0)T,(0,1,0,0)T, (0,0,1,0)T, (0,0,0,1)T}. Now, if S1 =span{(1,0,0,0)T,(0,1,0,0)T, (0,0,1,0)T }, then S1 is a subspace of R4 and S R4 . Further, S1 is of dimension 3. Also, if S2= span {(1,0,0,0)T,(0,1,0,0)T}, then S2 is a subspace of S1 and S1 S2 R4 with S1 S2 and S2 R4. The statement is False. We know that {e1,e2,e3,…en} is the standard basis for Rn, where each ei is a n-vector, and ei has 1 in the ith position, the rest of the entries being 0. Further, if m

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