Publications by Fares A
605_wk3discussion
Exercise #T10 in the PEE within chapter E of the book: Suppose that \(A\) is a square matrix. Prove that the constant term of the characteristic polynomial of \(A\) is equal to the determinant of \(A\). Solution The characteristic polynomial of a square matrix \(A\) of size \(n \times n\) is given by \[ p(\lambda) = \det(A - \lambda I) \] whe...
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605_wk3_discussionpostMichael
library(pracma) A <- matrix(c(3, 2, 1, 0, 1, 1, 1, 2, 0), nrow = 3, byrow = TRUE) char_poly <- charpoly(A) char_poly ## [1] 1 -4 0 5...
5 sym R (167 sym/2 pcs)
607_week3HW
df <- read.csv("https://raw.githubusercontent.com/fivethirtyeight/data/master/college-majors/majors-list.csv") Q1. Using the 173 majors listed in fivethirtyeight.com’s College Majors dataset, provide code that identifies the majors that contain either “DATA” or “STATISTICS” selected_majors <- df[grep("DATA|STATISTICS", df$Major, ignore...
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607_week1
Data 607 Week 1 assignment I chose the article titled “According To Super Bowl Ads, Americans Love America, Animals And Sex” which can be found at the URL https://projects.fivethirtyeight.com/super-bowl-ads/. Introduction The FiveThirtyEight analysis of Super Bowl ads reveals Americans’ affinity for themes of humor, patriotism, celebrities...
2011 sym R (3885 sym/7 pcs) 2 img
C31 post
Solving the problem posted by Jacob Silver: C31 Question C31 asks to solve the following set of linear equations: 3x + 2y = 1 x - y = 2 4x + 2y = 2 To solve this, we can use the matrix form of the equations: Matrix A: \[ A = \begin{pmatrix} 3 & 2 \\ 1 & -1 \\ 4 & 2 \end{pmatrix} \] Matrix B: \[ B = \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatri...
482 sym R (278 sym/2 pcs)
C22
Exercise C22 in chapter VS: Find the dimension of the subspace \(W\) of \(P_3\), given by: \[ W = \{ a + bx + cx^2 + dx^3 \mid a + b + c + d = 0 \} \] coeff_matrix <- matrix(c(1, 0, 0, -1, # polynomial a - d 0, 1, 0, -1, # polynomial b - d 0, 0, 1, -1), # polynomial c - d ...
157 sym
C51 exercise
C51, in the SSLE exercises of the Linear Algebra book Exercise C51: “Find all of the six-digit numbers in which the first digit is one less than the second, the third digit is half the second, the fourth digit is three times the third and the last two digits form a number that equals the sum of the fourth and fifth. The sum of all the digits ...
1515 sym