EXERCISE 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate base...
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them 2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
6 The use of cell phones, laptogs, and Poas s prohibited during the examination EXERCISE 1 [2.5/10] a) [1/10] Let &-((01,-1).(.1,). (1,0,1)) be a basis of R. Calculate the coordinates Of the vector 굿= +ē2 with respect to the basis B. (民=(6.G.G} is the canonical basis) [1,5/10] LetBe闻珂司andB"=(utuatust) be two bases of R3, where: b) Calculate the change of basis matrix from & to &. EXERCISE 2 (2.5/10] Given the following vector subspaces: 6 The use of cell phones, laptogs,...
2. Given the following three transactions T1 = r1(x); w1(y); T2 = r2(z); r2(y); w2(y); w2(x); T3 = r3(z); w3(x); r3(y); Consider the schedule S = r1(x); r3(z); r2(z); w3(x); r2(y); r3(y); w2(y); w1(y); w2(x); a. Draw the precedence graph of schedule S, and label each edge with data item(s). b. Based on the precedence graph, determine whether S is conflict serializable and justify your answer. If it is serializable, specify all possible equivalent serial schedule(s).
Consider the following transaction schedule: r1(X), r2(X), r3(X), r1(Y), w2(Z), r3(Y), w3(Z), w1(Y) This schedule is conflict-equivalent to some or all serial schedules. Determine which serial schedules it is conflict-equivalent to, and then identify a true statement from the list below. Select one: a. The schedule is conflict-equivalent to (T3, T1, T2) b. The schedule is not serial c. The schedule is conflict-equivalent to (T3, T2, T1) d. The schedule is conflict-equivalent to (T2, T3, T1) e. The schedule is...
EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the coordinates of the vector -el+e2 with respect to the basis B. (B. {e!, e2, e) is the canonical basis) [1.5/10] Let B-lul., иг, из} and B'-fu', ua",_} be two bases of R3. where : b) 3 Calculate the change of basis matrix from B to B' EXERCISE 1 [2.5/10] a) [1/10] Let B- [(0,1,-1), (1,1,1), (1,0,1)) be a basis of IR3. Calculate the...
10. Det ermine whether the following subsets W are subspaces of the given vect or spaces: (a) The set of 2 2 matrices given by W. A є M2.2 : A- as a subset of V M2,2 (b) The set of all 3 x 3 upper triangular matrices as a subset of V-M33- (c) The subset of vect ors in R3 of the for (2+x3, r2, r3). (d) The subset of vect ors in R2 of the form (ri,0) (e)...
Q4 (4 marks) Hand in c), d) only. Which of the following are vector subspaces of F4. a) {(x,y,z, w) € F4 : (x – 2y)(3z – 4w) = 1}. b) {(x, y, z, w) e F4 : (x – 2y)(3z – 4w) = 0} . c) {(1, Y, Z, W) € F4: (x – 2y) + (3z – 4w) = 1}. d) {(2, Y, Z, W) € F4: (x – 2y) + (3z – 4w) = 0}. :
Let F be the vector field on R3 given by F(x,y,z)=(2xz,-x,y^2) evalute the volume integral below. cheers 19. Let F be the vector field on R given by F(r,y,z) = (2xz, -x, y2) Evaluate 2xzdV, FdV xdV where V is the region bounded by the surfaces 0, y = 6, z = x2 and z = 4. 0, y
QUESTION 2 Consider the vector space R3 (2.1) Show that (12) ((a, b, c), (x, v, z))-at +by +(b+ c)(y + z) is an inner product on R3 (2.2) Apply the Gram-Schmıdt process to the following subset of R3 (12) to find an orthogonal basis wth respect to the inner product defilned in question 2.1 for the span of this subset (2.3) Fınd all vectors (a, b, c) E R3 whuch are orthogonal to (1,0, 1) wnth respect to the...
Q 1 Let V C R3 be the subspace V = {(x,y, z) E R3 : 5x 2y z 0} a) Find a basis B for V. What is the dimension of V? b) Find a basis B' for R3 so that B C B'