Publications by Bryan Persaud
Data 605 HW 3
Problem Set 1 What is the rank of the matrix A? A = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix}\) Solution: Reduce matrix A to row echelon form row 1 + row 2 to row 2 = \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 7 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{bmatrix}\) -5 * row 1 + row 4...
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Data 605 Discussion 3
Chapter Eigenvalues Section EE Exercise C26 For matrix A = \(\begin{bmatrix} 2 & 1\quad 1 \\ 1 & 2\quad 1 \\ 1 & 1\quad 2 \end{bmatrix}\) the characteristic polynomial of A is \(p_{ A }{ (X)\quad =\quad (4-x){ (1-x) }^{ 2 } }\). Find the eigenvalues and corresponding eigenspaces of A. Solution: Since we are given the characteristic polynomial of ...
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Data 605 Discussion 2
Chapter Determinants Section DM Exercise M11 Find a value of k so that the matrix A = [1 2 1 2 0 1 2 3 k] has det(A) = 0, or explain why it is not possible. Solution: First break down the 3x3 matrix into a 2x2 matrix by taking the number in row 1, column 1 and multiplying it by the 2x2 matrix not in the row and column of the number in row 1, colu...
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Data 605 HW 1
Problem Set 1 Calculate the dot product u.v where u = [0.5; 0.5] and v = [3; −4] u = [0.5; 0.5] and v = [3; −4] u · v = (0.5 * 3) + (0.5 * -4) = 1.5 + (-2) u · v = -0.5 What are the lengths of u and v? Please note that the mathematical notion of the length of a vector is not the same as a computer science definition. ||u|| = sqrt((0.5)^...
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Data 605 Discussion 1
Chapter Vector Section VO Exercise C15 Find α and β that solve the vector equation α [2 1] + β [1 3] = [5 0] (These are columns) Solution: Use definition CVA and definition CVSM to obtain a vector equation that we can use to make a system of equations. [5 0] = α [2 1] + β [1 3] = [2α + β α + 3β] By using definition CVE we can use the ve...
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Data 607 Final Project Presentation
Data 607 Final Project Presentation Bryan Persaud 12/11/2019 Introduction For my final project I am looking to analyze different food reviews. I love Japanese food it is my favorite type of food. I have always been curious to see if people feel the same way. This is my motivation for this project, to come to a conclusion to see if Japanese fo...
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Data 606 HW 9
Baby weights, Part I. (9.1, p. 350) The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. Here, we study the relationship between smoking and weight of the baby. The variable smoke is c...
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Data 606 Lab 9
Grading the professor Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related charac...
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Data 607 Final Project
library(tidyverse) ## -- Attaching packages ----------------------------------------------------------------------------------------------------------------------------- tidyverse 1.2.1 -- ## v ggplot2 3.2.1 v purrr 0.3.2 ## v tibble 2.1.3 v dplyr 0.8.3 ## v tidyr 1.0.0 v stringr 1.4.0 ## v readr 1.3.1 v forcats 0.4.0 ...
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Data 605 HW 2
Problem Set 1 Show that \({ A }^{ T }A \neq A{ A }^{ T }\) in general. (Proof and demonstration.) Solution: Proof: Suppose we have A that is a m x n matrix. The transpose of A, \({ A }^{ T }\), would be a n x m matrix. Using the definition of matrix multiplication, we can multiply \({ A }^{ T }\) by A which would result in a n x n matrix; a squ...
2241 sym R (877 sym/3 pcs)