# Create sample vectors and matrices vector_a <- c(1, 2, 3) vector_b <- c(4, 5, 6) matrix_A <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2) matrix_B <- matrix(c(7, 8, 9, 10, 11, 12), nrow = 2) # Vector addition vector_sum <- vector_a + vector_b cat("Vector A + Vector B:", vector_sum, "\n") # Vector subtraction vector_diff <- vector_a - vector_b cat("Vector A - Vector B:", vector_diff, "In") # Scalar multiplication scalar <- 2 vector_scaled <- scalar * vector_a cat("Scalar Multiplication:", vector_scaled, "In") # Dot product (inner product) of vectors dot_product <- sum(vector_a * vector_b) cat("Dot Product of Vector A and Vector B:", dot_product, "Vn") # Matrix addition matrix_sum <- matrix_A+ matrix_B cat("Matrix A + Matrix Biln") print(matrix_sum) # Matrix subtraction matrix_diff <- matrix_A - matrix_B cat("Matrix A - Matrix B:in") print(matrix_diff) # Matrix multiplication matrix_product <- matrix_A %*% matrix_B cat("Matrix A * Matrix B:ln") print(matrix_product) # Matrix transpose matrix_transposed <- t(matrix_A) cat("Transpose of Matrix Ailn") print(matrix_transposed) # Matrix determinant matrix_det <- det(matrix_A) cat("Determinant of Matrix A:", matrix_det, "In") # Matrix inverse matrix_inverse <- solve(matrix_A) cat("Inverse of Matrix A:in") print(matrix_inverse)