Module 6

1. Consider A=matrix(c(2,0,1,3), ncol=2) and B=matrix(c(5,2,4,-1), ncol=2).
a) Find A + B
b) Find A - B

> A=matrix(c(2,0,1,3),ncol=2)
> B=matrix(c(5,2,4,-1),ncol=2)
> A-B
     [,1] [,2]
[1,]   -3   -3
[2,]   -2    4
> A+B
     [,1] [,2]
[1,]    7    5
[2,]    2    2
(This concludes question 1) 

2. Using the diag() function to build a matrix of size 4 with the following values in the diagonal 4,1,2,3.
> diag(c(4,1,2,3), ncol=4)
     [,1] [,2] [,3] [,4]
[1,]    4    0    0    0
[2,]    0    1    0    0
[3,]    0    0    2    0
[4,]    0    0    0    3
(This concludes question 2) 

generate the following matrix: 

## [,1] [,2] [,3] [,4] [,5]
## [1,] 3 1 1 1 1
## [2,] 2 3 0 0 0
## [3,] 2 0 3 0 0
## [4,] 2 0 0 3 0
## [5,] 2 0 0 0 3

> diag(x=3, nrow=5, ncol=5)
     [,1] [,2] [,3] [,4] [,5]
[1,]    3    0    0    0    0
[2,]    0    3    0    0    0
[3,]    0    0    3    0    0
[4,]    0    0    0    3    0
[5,]    0    0    0    0    3
> m <-diag(x=3, ncol=5, nrow=5)
> sweep(m,1,c(1),"+")
     [,1] [,2] [,3] [,4] [,5]
[1,]    4    1    1    1    1
[2,]    1    4    1    1    1
[3,]    1    1    4    1    1
[4,]    1    1    1    4    1
[5,]    1    1    1    1    4

> m[1, ] + 1
[1] 4 1 1 1 1
> m[,1] + 2
[1] 5 2 2 2 2