Publications by Abdelmalek Hajjam/ Monu Chacko
DATA 605 Discussion 3
Exercises C10 Find the characteristic polynomial of the matrix \[ A= \left[ \begin{array}{cccc} 1 & 2 \\ 3 & 4 \end{array} \right] \] Answer library(pracma) A <- matrix(c(1, 3, 2, 4), nrow = 2) A ## [,1] [,2] ## [1,] 1 2 ## [2,] 3 4 A <- charpoly(A, info = TRUE) ## Error term: 4 A$cp ## [1] 1 -5 -2 The char...
986 sym R (175 sym/6 pcs)
DATA 605 HW 1
PROBLEM SET 1 Calculate the dot product u.v where u = [0.5; 0.5] and v = [3;−4] library(geometry) u <- c(0.5, 0.5) v <- c(3, -4) u.v <- dot(u,v,d = NULL) u.v ## [1] -0.5 \[ u = \left[ \begin{array}{cccc} 0.5 & 0.5 \end{array} \right] v = \left[ \begin{array}{cccc} 3 & -4 \end{array} \right] \] \[ u.v = (0.5 \tim...
2733 sym R (2157 sym/18 pcs)
DATA 605 Discussion 1
Exercises C20 Compute the product of the two matrices below, AB. Do this using the defnitions of the matrix-vector product (Defnition MVP) and the defnition of matrix multiplication (Defnition MM). \[ A= \left[ \begin{array}{cccc} 2 & 5 \\ -1 & 3 \\ 2 & -2 \end{array} \right] B = \left[ \begin{array}{cccc} 1 & 5 & -3 &...
2663 sym 3 tbl
Data 605 Discussion 2
Question 29: A student is applying to Harvard and Dartmouth. He estimates that he has a probability of .5 of being accepted at Dartmouth and .3 of being accepted at Harvard. He further estimates the probability that he will be accepted by both is .2. What is the probability that he is accepted by Dartmouth if he is accepted by Harvard? Is the eve...
746 sym
DATA 608 Assignment 1
Principles of Data Visualization and Introduction to ggplot2 I have provided you with data about the 5,000 fastest growing companies in the US, as compiled by Inc. magazine. lets read this in: inc <- read.csv("https://raw.githubusercontent.com/charleyferrari/CUNY_DATA_608/master/module1/Data/inc5000_data.csv", header= TRUE) # Import dplyr and gg...
1543 sym R (10198 sym/33 pcs) 3 img 2 tbl
DATA 605 HW 2
FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS Problem Set 1 Show that AT A != AAT in general. (Proof and demonstration.) Answer 1 Proof with out calculation The Commutative property of multiplication is not always true in a matrix multiplication. Order of multiplication matters. Lets say AT is a 5x2 matrix and A is a 2x3 matrix then its can be mul...
3798 sym R (4273 sym/12 pcs)
Discussion 4
C25 Define the linear transformation \[ T: C^3 \rightarrow C^2, T \left( \left[ \begin{array}{cccc} x1 \\ x2 \\ x3 \end{array} \right] \right) = \left[ \begin{array}{cccc} 2x1 & -x2 & 5x3 \\ -4x1 & +2x2 & -10x3 \end{array} \right] \] Verify that T is a linear transformation. Answer: Basic concept using exa...
2343 sym
Assignment 5
ASSIGNMENT 5 Choose independently two numbers B and C at random from the interval [0, 1] with uniform density. Prove that B and C are proper probability distributions.Note that the point (B,C) is then chosen at random in the unit square.Find the probability that Uniform Probability Distribution Prepare data n <- 1000 # Default min - 0 and max ...
761 sym R (1676 sym/25 pcs) 4 img
Linear Regression in R
Based on the video: https://www.youtube.com/watch?v=u1cc1r_Y7M0 mouse.data <- data.frame(weight=c(0.9, 1.8, 2.4, 3.5, 3.9, 4.4, 5.1, 5.6, 6.3), size=c(1.4, 2.6, 1.0, 3.7, 5.5, 3.2, 3.0, 4.9, 6.3)) mouse.data ## weight size ## 1 0.9 1.4 ## 2 1.8 2.6 ## 3 2.4 1.0 ## 4 3.5 3.7 ## 5 3.9 5.5 ## 6 4.4 3.2 ## 7 5.1 ...
70 sym R (1098 sym/5 pcs) 1 img