Determine whether each of the following is a subspace of the relevant R". (a) V1 =...
QUESTION 2. (a) Decide whether each of the following subsets of R’ is a subspace. Either provide a proof showing the set is a subspace of R3, or provide a counterexample showing it is not a subspace: [9 marks] (i) S= {(x, y, z) ER3 : 4.0 + 9y + 8z = 0} (ii) S = {(x, y, z) E R3 : xy = 0} (b) Determine for which values of b ER, the set S = {(x, y, z)...
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
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
please answer to all parts 4. In each case, determine whether W is a subspace of the F-vector space V. (a) F=Q, V =R2, and W = Z?. (b) F=R, V = RP, and W = {(x,y) ER?:zy >0}. (c) F=R, V = R', and W = {(x,y,z) € R3: x > 0, y > 0, 2 >0}. (d) F=R, V = C, and W = {(x, y, z) ECS:x + 2y + iz=0}. (e) F = Q, V =...
3. For each of the following sets, determine if it is a subspace of R3. If it is a subspace, prove it. If is is not a subspace provide an example showing how it violates at least one of the subspace axioms (a) B , y,z) E R3 (x, y, 2)l 1) (b) S (a b, 3b+ 2a,a-b) a, be R) [10 (c) P (7,5,8) s(1,-1,2)t (3, 1,4) s,te R)
4. For this question, we define the following matrices: 1-2 0 To 61 C= 0 -1 2 , D= 3 1 . [3 24 L-2 -1] (a) For each of the following, state whether or not the expression can be evaluated. If it can be, evaluate it. If it cannot be, explain why. i. B? +D ii. AD iii. C + DB iv. CT-C (b) Find three distinct vectors X1, X2, X3 such that Bx; = 0 for i =...
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.
Determine whether the subset S is a subspace of R" or not. If it is a subspace, explain why it is, either by checking that the three defining properties of a subspace are satisfied or by using a result from class (for insta that the span of vectors subspace which is not satisfied (e.g. specific vectors u and v are in S but iu ö is not in S), Studying examples 3.38, 3.39 and 3.40 in the textbook could be...
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...
Let v1,v2,v3 and v4 be linearly independent vectors in R4. Determine whether each set of vectors is linearly independent or dependent. Please solve d) and f) U1, 2, 03, 4