Publications by Gregg Maloy
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#install.packages("MASS") library(MASS) 1. What is the rank of matrix A. A =\(\begin{bmatrix}1 & 2 & 3 & 4 \\-1 & 0 & 1 & 3 \\ 0 & 1 &-2 & 1 \\ 5 & 4 &-2 &-3 \end{bmatrix}\) To solve we need row echelon form: Row operations Column 1: [2,1] must equal 0: Calculation: Row1+Row2 \(\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 7 \\ 0 & 1 &-2 ...
3285 sym R (834 sym/7 pcs)
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Find the characteristic polynomial of the matrix A. A =\(\begin{bmatrix}1 & 2 \\3 & 4\end{bmatrix}\) To solve we will use the equation det(A−λI)=0 A−λI =\(\begin{bmatrix}1-λ & 2 \\3 & 4-λ\end{bmatrix}\) Solve for λ: \[{det(A−λI)= (1-λ)(4-λ) - (2)(3) }\] \[{det(A−λI)=(λ^2-5λ+4)-6}\] \[{det(A−λI)=λ^2-5λ-2}\] Answer The ch...
375 sym
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Problem 1 Show that ATA != AAT in general. (Proof and demonstration.) Here is an example to demonstrate that ATA != AAT. The below 3 x 3 matrix A will be used to demonstrate ATA != AAT. library(matrixcalc) A<- matrix(c(2,-3, 4, 1, 0,1,2,1,2), nrow = 3, byrow = TRUE) A ## [,1] [,2] [,3] ## [1,] 2 -3 4 ## [2,] 1 0 1 ## [...
2238 sym R (2656 sym/30 pcs)
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A First Course in Linear Algebra, Beezer, R., 2008 Question C23 page 278: Doing the computations by hand, find the determinant of the matrix below. 1 3 2 4 1 3 1 0 1 Define matrix Below a 3x3 matrix is coded and printed. A <- matrix(c(1, 4, 1, 3, 1,0 ,2 ,3 ,1 ), nrow = 3, byrow = FALSE) print(A) ## [,1] [,2] [,3] ## [1,] 1 3 2 ...
530 sym
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A First Course in Linear Algebra, Beezer, R., 2008 C10, page 64 Compute matrix calculations Define matrix 1 matrix1 <- matrix(c(2, -3, 4, 1, 0), nrow = 5, byrow = TRUE) print(matrix1) ## [,1] ## [1,] 2 ## [2,] -3 ## [3,] 4 ## [4,] 1 ## [5,] 0 #Define matrix 2 matrix2 <- matrix(c(1, 2, -5, 2, 4), nrow = 5, byrow = TRUE) pr...
197 sym
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Part 1: Assignment & Packages One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment: 1.) Build the first letters for both your first and last na...
940 sym R (1911 sym/8 pcs) 81 img
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Assignment & Packages One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment: 1.) Build the first letters for both your first and last name using ...
871 sym R (2506 sym/8 pcs) 5 img
SMS Classification System Using TidyModels, Naive Bayes, Random Forest and XGBoost
Part 1: Assignment For this project, tidymodels was utilized to build a SMS classification system which flagged text messages as ‘spam’ or ‘ham’. Naive bayes, random forest and XGBoost models were then run to compare classification results across models. Part 2: Packages & Dataset The dataset used for this project is located at: https:/...
5286 sym R (16044 sym/41 pcs) 10 img
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Extend Assignment Overview The overarching purpose of this assignment was the utilization of github as a collaborative coding tool to explore push, pull, clone and forking capabilities. In this assignment a github repository was cloned, another student’s vignette .rmd file modified and then the .rmd file was pushed back to the original github...
4021 sym R (8473 sym/18 pcs) 4 img
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Part 1: assignment In this assignment, you’ll practice collaborating around a code project with GitHub. Using one or more TidyVerse packages, and any dataset from fivethirtyeight.com or Kaggle, create a programming sample “vignette” that demonstrates how to use one or more of the capabilities of the selected TidyVerse package with your se...
4101 sym R (8820 sym/18 pcs)