6. Consider the bipartite network below. 1 4 5 10 a Construct the adjacency matrix. Why is it a block-diagonal matrix? b. Construct the adjacency matrix of its two projections, on the purple and on the green nodes, respectively.
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- 2. Show the following cordinate frame matrix for cordinate space that has the following transform applied to it [order given, in global/world space]: rotation around the X axis of 30 degrees translation along (X=20,Y=10,Z=50) rotation around the Y axis of 135 degrees scaling factor of 6 along the Z axis translation along (X=50,Y=0,Z=50)If a matrix A has size 5x6 and a matrix B has a size 6x4, then what will be the size of a matrix A*B?If x=[1 4; 8 3], find :a) the inverse matrix of x .b) the diagonal of x.c) the sum of each column and the sum of whole matrix x.d) the transpose of x.
- a. Build an adjacency matrix ? for this map. b. How many paths of length 2 from V5 to V1 exist? c. How many paths of length 3 from V5 to V1 exist?In linear coding theory, there are such things as quaternary codes within the F_4 field. Question: What is an example of a quaternary code and its accompanying generator matrix (please provide matrix)?What is the implicit equation of the plane through 3D points (1,0,0), (0, 1, 0), and (0, 0, 1)? What is the parametric equation? What is the nor- mal vector to this plane? Given four 2D points a0, a1, b0, and b1, design a robust procedure to determine whether the line segments a0a1 and b0b1 intersect.
- Bu = ƒ and Cu = f might be solvable even though B and C are singular. Show that every vector f = Bu has ƒ1 + ƒ2+ ……. +fn = 0. Physical meaning: the external forces balance. Linear algebra meaning: Bu = ƒ is solvable when ƒ is perpendicular to the all – ones column vector e = (1, 1, 1, 1…) = ones (n, 1).Given a 2-D square matrix: ant mat{3}[{3]={{1, 2 3} {4,586}, {7.8.9FF Write a function transpose which Create a 3*3 matrix trans and store the transpose of given matrix in it.And prxnt the ' transpose, IN C++.Is the matrix diagonally dominant? if Not, make it diagonally dominant
- This is a question on Computer Graphics. Please provide a step-by-step solution. Question: Let (50, 70, 1500) be the coordinate of a light source of intensity 0.95 units. The light is illuminating a quad consisting of P0(10, 10, 5), P1(-10, 10, 5), P2(-10, -10, 6) and P3(10, -10, 6) vertices. Determine the intensity of the reflected light at the center of the quad using the diffuse reflection model. Given that the diffuse absorption coefficient of the quad surface is 0.8 unit.If there is a non-singular matrix P such as P-1AP=D, matrix A is called a diagonalizable matrix. A, n x n square matrix is diagonalizable if and only if matrix A has n linearly independent eigenvectors. In this case, the diagonal elements of the diagonal matrix D are the eigenvalues of the matrix A. A=({{1, -1, -1}, {1, 3, 1}, {-3, 1, -1}}) : 1 -1 -1 1 3 1 -3 1 -1 a)Write a program that calculates the eigenvalues and eigenvectors of matrix A using NumPy. b)Write the program that determines whether the D matrix is diagonal by calculating the D matrix, using NumPy. #UsePythonQuestion 18 .The following weighted graph corresponds to a railway network, determine the shortest way from station a to z