BCA PART B 4.R program to calculate simple linear algebra operations

Program :

# Function for matrix addition

matrix_add <- function(A, B) {

  return(A + B)

}

# Function for matrix subtraction

matrix_subtract <- function(A, B) {

  return(A - B)

}

# Function for matrix multiplication

matrix_multiply <- function(A, B) {

  return(A %*% B)  # Matrix multiplication in R uses the %*% operator

}

# Function to calculate the determinant of a matrix

matrix_determinant <- function(A) {

  return(det(A))

}

# Function to calculate the inverse of a matrix

matrix_inverse <- function(A) {

  if (det(A) != 0) {

    return(solve(A))  # solve(A) gives the inverse in R

  } else {

    return("Matrix is singular, inverse does not exist.")

  }

}

# Function to calculate the dot product of two vectors

vector_dot_product <- function(v1, v2) {

  return(sum(v1 * v2))  # Element-wise multiplication and summing it up

}

# Example matrices and vectors

A <- matrix(c(1, 2, 3, 4), nrow = 2, ncol = 2)  # 2x2 matrix

B <- matrix(c(5, 6, 7, 8), nrow = 2, ncol = 2)  # 2x2 matrix

v1 <- c(1, 2, 3)  # Vector 1

v2 <- c(4, 5, 6)  # Vector 2

# Performing operations

cat("Matrix A:\n")

print(A)

cat("\nMatrix B:\n")

print(B)

cat("\nMatrix Addition (A + B):\n")

print(matrix_add(A, B))

cat("\nMatrix Subtraction (A - B):\n")

print(matrix_subtract(A, B))

cat("\nMatrix Multiplication (A * B):\n")

print(matrix_multiply(A, B))

cat("\nDeterminant of Matrix A:\n")

print(matrix_determinant(A))

cat("\nInverse of Matrix A:\n")

print(matrix_inverse(A))

cat("\nDot Product of vectors v1 and v2:\n")

print(vector_dot_product(v1, v2)) 

Output :

Matrix A:

     [,1] [,2]

[1,]    1    3

[2,]    2    4

Matrix B:

     [,1] [,2]

[1,]    5    7

[2,]    6    8

Matrix Addition (A + B):

     [,1] [,2]

[1,]    6   10

[2,]    8   12

Matrix Subtraction (A - B):

     [,1] [,2]

[1,]   -4   -4

[2,]   -4   -4

Matrix Multiplication (A * B):

     [,1] [,2]

[1,]   23   31

[2,]   34   46

Determinant of Matrix A:

-2

Inverse of Matrix A:

     [,1] [,2]

[1,]   -2  1.5

[2,]    1 -0.5

Dot Product of vectors v1 and v2:

32

Explanation:

1. Matrix Addition (matrix_add):

   • Adds two matrices element-wise.

2. Matrix Subtraction (matrix_subtract):

   • Subtracts two matrices element-wise.

3. Matrix Multiplication (matrix_multiply):

   • Performs matrix multiplication using the %*% operator in R.

4. Determinant of a Matrix (matrix_determinant):

   • Computes the determinant of a matrix using the det() function.

5. Inverse of a Matrix (matrix_inverse):

   • Uses the solve() function to calculate the inverse of a matrix. If the determinant is zero, the matrix is singular and doesn't have an inverse.

6. Dot Product of Vectors (vector_dot_product):

   • Computes the dot product of two vectors using element-wise multiplication and then summing the results.