Assignment 6

 

Assignment 6: Matrix Operations and Construction

In this assignment, I practiced creating and manipulating matrices in R. The goal was to strengthen my understanding of how R handles matrix operations such as addition, subtraction, diagonal construction, and combining blocks of matrices to form structured arrays.

R Code

🔹 Task 1: Matrix Addition & Subtraction

# Task 1: define A and B

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

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

# Addition

A_plus_B <- A + B

print("A + B:")

print(A_plus_B)

# Subtraction

A_minus_B <- A - B

print("A - B:")

print(A_minus_B)

🔹 Task 2: Create a Diagonal Matrix

# Task 2: Create a Diagonal Matrix

D <- diag(c(4, 1, 2, 3))

print("Diagonal Matrix D:")

print(D)

🔹 Task 3: Construct a Custom 5×5 Matrix

# Task 3: Construct a Custom 5x5 Matrix

# Step 1: create the first row

row1 <- c(3, 1, 1, 1, 1)

# Step 2: create the remaining rows:

# - first column all 2’s (rows 2–5)

# - diagonal of 3’s starting from row 2

block <- diag(3, 4) # 4x4 identity scaled by 3

col_block <- matrix(2, nrow = 4, ncol = 1)

rest <- cbind(col_block, block)

# Step 3: combine row 1 with the rest

M <- rbind(row1, rest)

print("Custom 5x5 Matrix M:")

print(M)

Output

Matrix Addition & Subtraction: For addition and subtraction, R performs element-by-element operations. Each corresponding entry in matrix A and matrix B is added or subtracted to produce a new matrix of the same dimensions.

ADDITION: Adding two matrices results in a new matrix where each element is the sum of the corresponding elements from the original matrices.

SUBTRACTION: Subtracting one matrix from another results in a new matrix where each element is the difference between the corresponding elements of the original matrices.

Diagonal Matrix (diag()): The diag() function creates a square matrix with specified values on the diagonal and zeros elsewhere. This is useful for creating identity matrices or scaling diagonal elements.

Custom 5×5 Matrix Construction: This matrix is built by combining a custom first row with a block structure. It uses a column of repeated values and a diagonal matrix to fill the rest.

• rbind() (Row Bind):
  The rbind() function in R combines two or more matrices or vectors by stacking them row-wise, adding new rows to the existing matrix.

• cbind() (Column Bind):
  The cbind() function combines matrices or vectors column-wise, adding new columns side by side to form a larger matrix.

Conclusion

This assignment strengthened my understanding of how R handles matrix structures and arithmetic. By performing matrix addition and subtraction, I learned the importance of dimension compatibility in operations. Constructing a diagonal matrix using diag() helped me see how R efficiently represents data along specific axes, while building a custom 5×5 matrix reinforced how rbind() and cbind() can be used to combine and organize matrix components programmatically.