Module # 6 Doing math in R part 2

1. Matrix Operations

Given two matrices:

A <- matrix(c(2, 0, 1, 3), ncol = 2)
B <- matrix(c(5, 2, 4, -1), ncol = 2)

a) Find A + B

To find the sum of matrices A and B, simply add corresponding elements:

A + B

Output:

     [,1] [,2]
[1,]    7    2
[2,]    5    2

Explanation:
The sum of the matrices is calculated element by element:

(2 + 5) = 7
(0 + 2) = 2
(1 + 4) = 5
(3 + -1) = 2

b) Find A - B

To find the difference between matrices A and B, subtract corresponding elements:

A - B

Output:

     [,1] [,2]
[1,]   -3   -2
[2,]   -3    4

Explanation:
The difference of the matrices is calculated element by element:

(2 - 5) = -3
(0 - 2) = -2
(1 - 4) = -3
(3 - -1) = 4

2. Creating a Diagonal Matrix

To build a 4x4 matrix with the diagonal values 4, 1, 2, and 3 using the diag() function.

diag(c(4, 1, 2, 3), nrow = 4)

Output:

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

Explanation:
The diag() function is used to create a matrix with the specified values on the diagonal. In this case, the matrix is 4x4, and the numbers 4, 1, 2, and 3 are placed on the diagonal, with all other elements being zero.

3. Generate the Specified Matrix

To generate a 5x5 matrix where the first row starts with a 3 and is followed by four 1’s. The diagonal has values of 3, and the other values are 2. The structure should look like this:

matrix_data <- diag(3, 5)  
matrix_data[1, 2:5] <- 1   
matrix_data[2:5, 1] <- 2   
matrix_data

Output:

     [,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

Explanation:

By creating a 5x5 matrix with 3's along the diagonal using diag(3, 5).
Then, modify the matrix: The first row is updated with four 1’s starting from the second column, and the first column (from row 2 to 5) is filled with 2’s.

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