week5.Rmd

---
title: "Week 5 R Quiz"
author: "dan berko"
date: "July 5, 2014"
output: html_document
---
Question 1
--------
```{r, matrixCreation, prompt=TRUE, eval=TRUE}
A <- matrix(c(1,-1,-1,-1), nrow=2)
A
B <- matrix(c(2, -1, 3, -2), nrow=2)
B
C <- matrix(c(1, 0, 0, 0), nrow=2, ncol=2)
C
D <- matrix(c(0, 1, 0, 1, 0, 0, 0, 0 ,1), nrow=3)
D
E <- matrix(c( 1, 0, 0, 0, 0, 1, 0, 1, 0), nrow=3)
E
```
Question 2
--------
```{r, idempotent, prompt=TRUE, eval=FALSE}
A %*% A == A
B  %*% B == B
C %*% C == C
D %*% D == D
E %*% E == E
```
Only C is an idempotent matrix

Question 3
--------
```{r, orthogonal, prompt=TRUE, eval=FALSE}
t(A) == solve(A)
t(B) == solve(B)
t(C) == solve(C)
t(D) == solve(D)
t(E) == solve(E)
```
D and E are orothogonal matrices

Question 4
--------
```{r, listCreation, prompt=TRUE, eval=TRUE}
V <- c('fee', 'fi', 'fo', 'fum')
A <- array(17:51, dim=c(5,7))
L <- list(1, 'potato', 2, 'potato', 3, 'potato', 4)
newList <- list (V, E, A, mtcars, L)
newList
```