Suppose we have three points in a two dimensional space: (3,1), (2,1), and (7,7). We want to perform PCA on these points, so we construct a 2-by-2 matrix whose eigenvectors are the directions that best represent these three points. Construct this matrix, as outlined in the PCA algorithm discussed in class, and identify, in the list below, one of its elements. O a) 25.5 O b) 14 O c) 27 O d) 12
Q: A: If x=[ 26 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…
A: answer : Average value of row 1 = (2+6+12)/3=20/3=6.6667 A) replaced matrix…
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A:
Q: If x= [ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its…
A: Since no programming language is mentioned, I am using matlab Code: format shortGx=[2 6 12;15 6 3;10…
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A: Below i have calculated first 3 PART.
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- The goal of this problem is to walk from cell (0, 0) to cell (m, n) of a two-dimensional array. Each step must be either to the right or downward. So you can step from cell (1, 1) to cell (1, 2) or (2, 1). but not from (1, 1) to (0, 1) or (1,0). You are given a toll matrix, where each cell contains a toll that must be paid upon entry into that cell. The goal is to make it from cell (0, 0) to cell (m, n) while paying the smallest possible total toll. Does a greedy algorithm work? Think it out. Write a dynamic programming algorithm that finds the minimum possible total toll. It does not need to do reconstruction and say how to achieve that total toll.Suppose a computer program needs to apply an affine transformation to a complex three-dimensional object made up of 3000 points. The transformation is composed of 8 matrices (call them M1 through M3), so for each point (x, y, z) in the object, the following operation is performed. |-|-|-|-|| y M1 M2 M3 M7 M8 Each multiplication of a matrix times a column vector involves 16 multiplications (of one number by another) and 12 additions, for a total of 28 arithmetic operations. Each multiplication of a matrix times another matrix involves 64 multiplications and 48 additions, for a total of 112 arithmetic operations. (These numbers are not made up or chosen randomly; they are facts about 4 x 4 matrix multiplication.) The most inefficient way of applying the transformation to the 3000 points would be to begin on the left, multiplying M1 by M2, then that result by M3, and so on along the list from left to right, and doing the same 8 multiplications again for each of the 3000 points. How many…Given a vector x=[12 3 4 5 . ], take the square of each element and sum them up. What should be the dimension of the vector x so that the squared sum (as above) is as close as possible to 1000 but not more than 1000? ....
- Write a program that can inverse a matrix by using an approach to find its minor, cofactor and adjugate matrix. Test your program with the given matrix ?Create a 3-by-3 matrix. A = [1 7 3; 2 9 12; 5 22 7]; Calculate the right eigenvectors, V, the eigenvalues, D, and the left eigenvectors, W. [V,D,W] eig(A) %3!use my ID : 201909010 SOLVE ALL BY matlab Consider the graphs of the functions f(x) = m - 1x and g(x) = 2x² — n where m and n are the maximum and mean values of the digits in your student-ID number. a) Create a vector v whose elements are the digits of your student-ID number. b) Create a variable m and assign the maximum digit in v to it. Create a variable n and assign the mean value of the digits in v to it. d) Define the function f(x) and g(x) above as anonymous functions. Plot the graphs of f(x) and g(x) on the same figure using the MATLAB function ezplot. f) Find the exact values of the x-coordinates of the intersection points between the two graphs using the MATLAB function solve. g) Find the area bounded by the two graphs.
- Generate a 1×2500 vector of random numbers using the function rand(). Extract the 1st, 2nd, 4th, 8th, 16th, …, 2048th elements and assign it as vector G. Do not use loops. Write the answer in the space provided.Given a Matrix A, • Create a row vector of 1's that has same number of elements as A has rows. • Create a column vector of 1's that has the same number of elements as A has columns. Using matrix multiplication, assign the product of the row vector, the matrix A, and the column vecto (in this order) to the variable result. Think about what the result represents...This problem is on Computer Graphics and is based on the topic 'Perspective Projection'. Please provide a step-by-step solution to the problem and explain the steps. The solution must include the General purpose perspective projection matrix. Question: Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.
- In a company, there are several branches. Let us consider a branch of that company having N employees, if the manager is allotted to that branch(s) then he is known to everyone else in that branch. Note that the property of "known to everyone" is unique to a manager. Your task is to find the manager in that branch. Input from the user in main ( ), the square matrix M where if an element of row i and column j is set to 1 it means that ith person knows jth person. You need to write a function managerId ( ) which returns the id of the manager if present or else returns -1. The function managerId ( ) takes two arguments - the square matrix of N *N and its size N. Call managerId ( ) from the main ( ) output the information about the manager. Assume all diagonal elements to be 1 (as everyone knows him/herself) and there is at most one manager in the company.Q1. Design a generic matrix multiplier. Here ‘generic’ means the design should work for anymatrix multiplication X∙Y = Z, where the matrices X, Y, and Z are of sizes a×b, b×c, and a×crespectively. Now, pick a, b, c from the last three digits of your roll number. ( If any of the digitsis 0, take 3 instead of it; if two digits are 0s, then take 3 for the first 0, and 5 for the second 0)For Example, if the last three digits are 123 then a = 1, b = 2, and c = 3; if the last three digitsare 204 then a = 2, b = 3, c = 4; f the last three digits are 100 then a = 1, b = 3, c = 5.Help the lazy mountain climber. Assume that a mountain climber wants to cross a mountain range by limiting the change in elevation (i.e., the climber does not want to climb up or down more often than necessary). The elevation of the terrain is given in a m by n matrix. The climber needs to start in the first column and end in the last column. Each move can be to the right, to the right and up, or to the right and down. Construct an algorithm to determine the minimum change in altitude that is possible for crossing the mountain range. State the time efficiency of your approach