2 is the question Question 4 [35 marks in total] An n xn matrix A is...
Question 4 [35 marks in totalj An n x n matrix A is called a stochastic matrix if it! satisfies two conditions: (i) all entries of A are non-negative; and (ii) the sum of entries in each column is one. If the (,) entry of A is denoted by any for ij € {1, 2,...,n}, then A is a stochastic matrix when alij 20 for all i and j and I j = 1 for all j. These matrices are...
Let A-(Aij)i iJSn є {0,1)"xn denote the symmetric adjacency matrix of an undi- rected graph. For iメj, we have Aij = 1 if entity i and j are connected in a network and 0 otherwise: A 0, i-1,..., n. The stochastic block model (SBM) postulates where is a full rank symmetric K x K connectivity matrix with entries in [0, 1]. a) Consider the matrix P-M MT, where M {0,1)"xK denotes the community k-1,... , K. Show that under (1),...
About linear algebra,matrix; 2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 x 9 matrices. The (i.j)-entry of the matrix B is given by i *j -1. The (i. j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? ii. Is vector u 9,64,-71,...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a matrix A = (aij) E Matn,n(F) and i < n let 1 row,(Α-Σ@y and col,(A)-Žaji CO j-1 j-1 be the sum of entries in row i and column i, respectively. Define C, A EMat,,(F): row,(A)col,(A) for all 1 < i,j < n] C, { A E Matn.n(F) : row,(A) = 0 = col,(A) for...
[8 marks] Consider a discrete time stochastic process {Xn,n 2 0j defined by the equation with Xo1 and Rn,n21 are random variables taking their values in (-1,00). Denote Sn-Li-1 Rk for n 〉 1 and So-0 i) [3 marks] Briefly explain why the filtration {F,:n 〉 0} gener- 0 generated by ated by Xo, X1,.. . , Xn and the filtration , n So, S1, , Sn should be identical ії) [5 marks] Show that {X,,n 〉 0} is a...
QUESTION 3 (10 Marks) Suppose you are given an array A[0..n 1 of integers, each of which may be positive, negative, or zero. A contiguous subarray A|i..j] which includes all the items starting at array index i and ending at array index j is called a positive interval if the sum of its entries is at least zero. For example let A-{-1, 3,-5, 2, 0,-4, 3,-6,-2). Ten A[3, 6) is a positive interval since its sum is 2+0+(-4)+3-1, but Al4,7isnot...
Due in 2 hr (a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
please answer 2a(i) only 2. (a) Use Octave as a Calculator to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j - 1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? ii. Is vector u- [9,...
Can you help me with this question please? For the code, please do it on MATLAB. Thanks 7. Bonus [3+3+4pts] Before answering this question, read the Google page rank article on Pi- azza in the 'General Resources' section. The Google page rank algorithm has a lot to do with the eigenvector corresponding to the largest eigenvalue of a so-called stochastic matrix, which describes the links between websites.2 Stochastic matrices have non-negative entries and each column sums to1, and one can...