Question

(C) Find a basis for the null spac Problem 5. (10 pts.) Determine which of the following statements are correct. Circle one: (a) True False Let V be a vector space, and dimension of V = 2. Then it is possible to find 3 linearly independent vectors in V. (b) True False Let vector space V = span{01, 02, 03}. Then vectors 01, 02, 03 are linearly independent Page 2 (c) True False Lete. Eg and eg be a basis of vector space V. Then dim V - 3 (d) True False Let vectors from the vector space. V be lincarly mdepen dent. Then dimension of V = 3. (c) True False Let vectors t o my from the sector space be linearly indepen dent and any vectors from this spaer be lincarly Wependent. Then dimension of

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Answer 1

False Beca oll Because Maximal lneodly independent set of vecters form a basis If dim v=2 then maximum a vecter an linearly indo an - V21 Spon (Y, V2, Vs) = v False = R² (R) Spon of (0,0), (1), (6,1)=v But these 3 ore LoD due to zero recter e, ez ez are basis of us dim v= Numbes of element O in basis False e,= U1 = { (10),(0,1)] ezz {(1,1), 6.13 .. l = {(2, 1) (3,1)] Cs Scanned witive basis for R2 But dim QY=2 Scanned wiony CamScanner

False 0={[:]} OOO- ve R" ((R) dim v=4 maximal linearly independent set of vectes form a basis [ dim v=3 True Scanned with CamScanner