(1) Show that $A^TA\neq AA^T$ in general. (Proof and demonstration.) (2) For a special type of square matrix A, we get AT A = AAT . Under what conditions could this be true? (Hint: The Identity matrix I is an example of such a matrix). Please typeset your response using LaTeX mode in RStudio. If you do it in paper, please either scan or take a picture of the work and submit it. Please ensure that your image is legible and that your submissions are named using your first initial, last name, assignment and problem set within the assignment. E.g. LFulton_Assignment2_PS1.png

Doing the computations by hand, nd the determinant of the matrix below.  1 3 2 6

# Meaningful question for analysis: Do students do better in Math or Reading? # This data set contains Test score information for counties in California. My conclusion is that the average test score is 650 across both Reading and Math. Students do equally well in both subjects.

R Bridge Course Week 2 Assignment One of the challenges in working with data is wrangling. In this assignment we will use R to perform this task. Here is a list of data sets: http://vincentarelbundock.github.io/Rdatasets/ (click on the csv index for a list) Please select one, download it and perform the following tasks: 1. Use the summary function to gain an overview of the data set. Then display the mean and median for at least two attributes. 2. Create a new data frame with a subset of the columns and rows. Make sure to rename it. 3. Create new column names for the new data frame. 4. Use the summary function to create an overview of your new data frame. The print the mean and median for the same two attributes. Please compare. 5. For at least 3 values in a column please rename so that every value in that column is renamed. For example, suppose I have 20 values of the letter “e” in one column. Rename those values so that all 20 would show as “excellent”. 6. Display enough rows to see examples of all of steps 1-5 above. 7. BONUS – place the original .csv in a github file and have R read from the link. This will be a very useful skill as you progress in your data science education and career. Please submit your .rmd file and the .csv file as well as a link to your RPubs.

R Bridge Week 1 Assignment Please create the following exercises in .rmd format, publish to rpub and submit both the .rmd file and the rpub link. 1. Write a loop that calculates 12-factorial 2. Show how to create a numeric vector that contains the sequence from 20 to 50 by 5. 3. Create the function “quadratic” that takes a trio of input numbers a, b, and c and solve the quadratic equation. The function should print as output the two solutions.