true or false, justify your answer (B)The vectors (1,1,1,0), (1,1,0,0), and (1,0,0,1) form a basis in...
6.2.24 Justify each Assume all vectors are in R. Mark each statement True or False. Justify each answer a. Not every orthogonal set in Rn is linearly independent. O A. False. Orthogonal sets must be linearly independent in order to be orthogonal. O B. True. Every orthogonal set of nonzero vectors is linearly independent, but not every orthogonal set is linearly independent. O C. False. Every orthogonal set of nonzero vectors is linearly independent and zero vectors cannot exist in...
3)True or false? ( Justify your answer). a)6sven 6 b)10101wo 2121hree
3)True or false? ( Justify your answer). a)6sven 6 b)10101wo 2121hree
(a) (5 points.) Let W CW CW CW3 be distinct subspaces of R? True/False (Justify your answers): (i) Wo must be the zero subspace. (ii) W, must be R. (iii) W, must be RP. (iv) Suppose V1, V2, V3 are vectors such that vi EWW -for each 1 <i<3. Then {V1, V2, V3} must be a basis for R. (v) There are three linearly independent vectors in R that do not form a basis for R?
Determine if the statement is true or false, and justify your answer. If u4 is not a linear combination of {u1, u2, u3}, then {u1, u2, u3, u4} is linearly independent. A) False. Consider u1 = (1, 0, 0), u2 = (0, 1, 0), u3 = (0, 0, 1), u4 = (0, 1, 0). B) False. Consider u1 = (1, 0, 0), u2 = (1, 0, 0), u3 = (1, 0, 0), u4 = (0, 1, 0). C) True. The...
Justify your answer with brief comments please.
True or False. The two monomers a and b react to form the polycarbamate/polyurethane palymer e below. Justify your answer with appropriate comments HO
Determine if the statement is true or false, and justify your answer. If u1, u2, u3 is linearly independent, then so is (ui, u2. u3. u4) True. If u1. u2, u3ł is linearly independent, then the equation xu1 + xzu2 + x3u3 0 has a nontrivial solution, and therefore so does x1U + xzu2 x3u3 False. Consider for example u1 = 0 False. Consider for example u4 = 0. True. The echelon form of the augmented matrix [u1 u2 u3...
7. (0.2 pts) Answer True/False and justify your answer. a) b) (0.1 pts) Double-stranded RNA preferentially form B-form polymers (0.1 pts) The dipoles of water molecules decrease the strength of other electrostatic interactions
Determine whether the following statements are True or False. Justify your answer with a proof or a counterexample as appropriate. (a) The relation Son R given by Sy if and only if 1 - YER - N is an equivalence relation. (b) The groups (R,+) and (0,0), :) are isomorphic.
4. H ere are some True/False questions. If your answer is "TRUE", there is no need to justify your answer. If your answer is "FALSE", then you should justity your answer with a counterexample or explanation. There are also some "short-answer" questions. . A. (True-False). Every simple field extension of K is a finite field extension. . B. (True-False). Let R⑥ F be a field extension. Suppose that F is a of u E F, and splitting field for the...
True-False Questions: Justify your answers. In these questions, assume that R is the reduced echelon form of the augmented or a system O 1.20 If the system has three unknowns and R has three nonzero rows, then the system has at least one solution. 1.21 If the system has three unknowns and R has three nonzero rows, then the system can have an infinite number of solutions. of colntions