A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A2 and A3 are given below. 0 0 1 0 0 0 0 0 1 0 A² = 0 0 0 0 1 A3= 10100 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 10100 0 1 0 1 0 0 0 1 0 1 Which edge is not in the transitive closure of G? (2,4) ○ (5,5) ○ (1,3) ○ (4,5)

Q: Which matrix represents the number of walks of length 2 and how many walks of length 2 are in the…

A:

Q: Let D be an n×n diagonal matrix whose diagonal entries are either 0 or 1. i. Show that D is…

A: The matrix D will be idempotent iff Since  is the matrix where each diagonal entry is square of 0…

Q: 1. A matrix is symmetric if for each pair of indices i and j, the i, j entry equals the j, i entry.…

A: We recall the definitions of symmetric matrix which is A=A^T

Q: Let = Find a nonsingular matrix P and a diagonal matrix D such that P-'AP = D.

A:

Q: -1 -1 -1 -1

A: Just consider linear combination and then see the scalars are zero or nonzero.

Q: Find the adjacency matrices for the directed graphs in (a) and (b). (a) V2 La

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: then

A: Both statements 1 and 2 are TRUE, the proof of each of the statement is given in step 2.

Q: 6. If A is an invertible matrix, show that its projection matrix, P, is the identity matrix, I.

A:

Q: 2. Use row operations to transform the following matrix 1 0 -1 1 012 4 in the form 001 −1 1 2 4 b…

A: Given matrix is

Q: Consider the COO format of a sparse matrix A: A. data = [0.30 0.40 0.20 0.80 0.20 0.60 0.40 0.80] A.…

A: Given the  COO format for the sparse matrix A, we have:A.data = [0.30, 0.40, 0.20, 0.80, 0.20, 0.60,…

Q: Let A and P be a nxn matrices and P is invertible. Show that A and PA have the same rank

A:

Q: The following data matrix represents a simple closed polygon. 08500 0 0 1 0 0 A = Draw the figure.…

A:

Q: Given A is a 2 x 2 matrix for any x € R². a) Write a matrix B to represent a reflection of x across…

A:

Q: (12) A directed graph has the following adjacency matrix: [1 0 21 |2 1 0| [0 2 1] How many edges…

A:

Q: [a b el lef g 1. Consider the augmented matrix where a, b, c, d, e, f.g.heR. (a) Using Using *s, 1s,…

A:

Q: 3. Find the adjacency matrix of the intersection of W4 and K5. What is the degree of vertexes in W4…

A:

Q: Let A be the adjacency matrix of a graph G = (V,E). Moreover, let A' = D number of zero entries in…

A: Let A be an Adjacency MAtrix of a graph G=(V,E) Moreover, Let A'=∑i=1v-1Ai and x be the number of…

Q: Find an invertible matrix U such that UA = R is the REEF of A, fo [21 A = 3 -1 1-2 -1 0 2 1 3 1 .

A: