Question 4 (10 marks) t possible to co (a) Col A and Row A; (b) Row A and NulA; (c) Nul A and Col A. Justify the answer...
Consider 01 0 A 1 20 4 (a) Find a basis for Row A and Nul A and hence find the dimension of each. (b) Is (-2,1,1) in Nul A? Justify your answer. Consider 01 0 A 1 20 4 (a) Find a basis for Row A and Nul A and hence find the dimension of each. (b) Is (-2,1,1) in Nul A? Justify your answer.
SECTION B (4 QUESTIONS, 90 MARKS) Question 4. [32 marks in total] For this question, assume the definition of Java class Heap given in the Appendix. The heaps referred to in this question are all maxHeaps. a. (5 marks) Insert into an empty (binary) heap the values 35, 4, 72, 36, 49, 50. Draw all intermediate steps b. (3 marks) Carry out one deletion operation on the final heap in (a.) above. c. (2 marks) Give the worst-case time complexity...
+ Question Details 2 1 , and A = | V1 V2 V3 | . Is p in Nul A? Let v,-| 0 2 Yes, p is in Nul A No, p is not in Nul A 5.+ Question Details 2 2 10 2 1 0 30 0 2 41 4 2 16 3 Let A so that an echelon form of A is given by . Find a basis for Col A 1 0 3 1 0 0 0...
Question 2 (10 marks) If z6 = 22%, calculate each of (a), (b) and (c) below. Show your working. (a) 0.58. Give your answer to 3 significant figures. [4 marks] (b) ;(5). Give your answer to 4 significant figures. [2 marks]
(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is an n×n invertible matrix and AB is an n×n invertible matrix, then B is an n × n invertible matrix, for all natural numbers n. [4 marks] (iii) det(A) = 1 for all invertible matrices A that satisfy A = A2....
Question 4 (10 marks) When analysing the complexity of algorithms, there are three main approaches: worst case, best case and average case. As an example, consider measuring the complexity of list-merging by counting the number of comparisons used As a test example, assume the following A1: There are two ordered lists, each of length 4, say A2: Neither list contains repeats, so a! < a2 < аз < a4 and bl <b2 < b3 < b4 A3: The lists are...
7. If possible, give an example of a linear transformation T: M22 P2 (and justify) so that (a) T is one-to-one (b) T is not one-to-one but onto (c) T is neither one-to-one nor onto
Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation (4+12) -CO Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t)= Skipped Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation (4+12) -CO Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t)= Skipped
4. (10 marks) (Black-Scholes) Fill in the details of L9.24. Specifically, a. (3 marks) Assume that C(S, t) satisfies the first PDE of L9.24 (Black-Scholes). Show that U(z,T) satisfies the second PDE of L9.24 (the heat/diffusion equation b. (5 marks) Using L9.23, solve for U Write your final answer using the standard normal CDF N Hint: Replace the lower limit of integration (the -o) with a correctly chosen quantity that lets you get rid of the "positive-part function" in the...
a 10 question multiple choice test has 4 possible answer for each question. A student selects at least 6 correct answers.Find probability of this event:(multiple choice)A) .118B) .995C) .068D) .571
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