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...
5 3 1 0 Problem 10 Let wi = ,W2 W3 Let W = Span{W1,W2, W3} C R6. 11 9 1 2 a) [6 pts] Use the Gram-Schmit algorithm to find an orthogonal basis for W. You should explicitly show each step of your calculation. 10 -7 11 b) [5 pts) Let v = Compute the projection prw(v) of v onto the subspace W using the 5 orthogonal basis in a). c) (4 pts] Use the computation in b) to...
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'
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).
uiaL1 Wi and S : R2 → R2 projects vectors onto the z-axis. 2 0 20. (6 points) Let H= AEM2x2 : (a) Given that H is a subspace, find a basis for it. (b) What is the dimension of H? (c) Can:] be written as a linear combination of your basis vectors? Justify. OT
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 2 [2.5/10] Given the following vector subspaces: W, Ξ {(x, y, z) E R3 / 0) x + y a) [1.0/10] Calculate bases of Wi and W2. b) [1.0/10] Calculate a basis of W1 n W2 c) [0.5/10] Calculate a basis of W1 + W2 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 bases of Wi and W2. b) [1.0/10] Calculate a basis of...
Question 5. (20pts) (Briefly justify your answer) 1) Consider three transactions: T1, T2 and T3. Draw the precedence graph for the following schedule consisting of these three transactions and determine whether it is conflict serializable a) (5points) S: R1(X); R3(Z); W2(X); RI(Z); R3(Y); W2(Y), R3(Z), W1(Z), b) (5points) S: RI(X); R3(Z); W20x); RI(Y); R2(Y); W3(Y); R3(Z); WI(Z);
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
Linear Algebra Problem! 1. Let U be the subspace of R3 given by 11 + 12 - 213 = 0. for U. Justify that is an ordered basis. What is the a) Find an ordered basis dimension of U? b) Let ū= (1,1,1). Show that ✓ EU and find the B-coordinate vector (Ū3 = C:(Ū), where Ce: U + R2 is the B-coordinate transformation.
linear algebra 2. Which of the following subsets of Rare actually subspaces? Justify your answer in terms of the definition and properties of subspaces. (a) The vectors [x y z]" with x + 2y -z = 0. (b) The vectors [a b c]" with a + b + c = 3. (c) The vectors [a+2bb-3b]' where a, b are any real numbers, (d) The vectors [pr] where q.r are any real numbers and p20.