(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector...
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
(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?
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x - y = 1) is a subspace of vector space V - R 3. Let vi, V2, V3 be three linearly independent vectors in a vector space V. Is the set {v1 - 2v2, 2v2 - 3v3, 3V3 - Vi} linearly independent or linearly dependent? Prove your answer.
Can u please answer the question (G) 1. (15 marks total) Consider the real vector space (IR3, +,-) and let W be the subset of R3 consisting of all elements (z, y, z) of R3 for which z t y-z = 0. (Although you do not need to show this, W is a vector subspace of R3, and therefore is itsclf a rcal vector space.) Consider the following vectors in W V2 (0,2,2) V (0,0,0) (a) (2 marks) Determine whether...
Homework: Section 4.1 Score: 0 of 1 pt 4.1.13 3 4 11 Let v1 0 , V2|1 V3 3 and w= 1 1 4 10 Is w in {v,, v2, v3}? How many vectors are in {v,, v, V3}? b. How many vectors are in Span{v, V2, V3}? c. Is w in the subspace spanned by (v,, v2, V3)? Why? a a. Is w in {v, V2 V31? O A. Vector w is in {v,, v2, V3} because it is...
Can I get help with questions 2,3,4,6? be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
1) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the vectors v1, v2, v3 linearly dependent or independent? justify your answer Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
7. In each part of this problem a set of n vectors denoted V, , denoted V. Carefully follow these directions V, is given in a vector space i) Determine whether or not the n vectors are linearly independent. i) Determine whether or not the n vectors are a spanning set of V Then find a basis and the dimension of the subspace of V which is spanned by these n vectors. (This subspace may be V itself.) a. V...
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
Let v1= [−3 0 6]T , v2= [−2 2 3]T , v3= [0 − 6 3]T , and w= [1 14 9]T . (1). Determine if w is in the subspace spanned by v1, v2, v3. (2). Are the vectors v1, v2, v3 linearly dependent or independent? Justify your answer.