Sample Programs Using Matrices in R

 

Sample Programs Using Matrices in R

The following programs demonstrate practical numerical applications of matrices suitable for undergraduate laboratories.

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1. Student Mark Analysis

Problem

Marks of 4 students in 3 subjects are stored in a matrix. Find:

• Total marks of each student.
• Average marks of each student.
• Highest mark in each subject.
• Class average in each subject.

Program

marks <- matrix(
  c(85,90,78,
    92,88,80,
    75,82,85,
    95,91,89),
  nrow=4,
  byrow=TRUE
)

print(marks)

# Total marks of students
totals <- rowSums(marks)

# Average marks of students
averages <- rowMeans(marks)

# Highest mark in each subject
highest <- apply(marks,2,max)

# Subject averages
subject_avg <- colMeans(marks)

cat("Total Marks:\n")
print(totals)

cat("Average Marks:\n")
print(averages)

cat("Highest Mark in Each Subject:\n")
print(highest)

cat("Subject Averages:\n")
print(subject_avg)

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2. Matrix Multiplication

Problem

Compute the product of two matrices.

Program

A <- matrix(c(1,2,3,4),2,2)

B <- matrix(c(5,6,7,8),2,2)

print(A)
print(B)

C <- A %*% B

cat("Product Matrix:\n")
print(C)

Output

     [,1] [,2]
[1,]   23   31
[2,]   34   46

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3. Solving a System of Linear Equations

Problem

Solve

$$2x+y=5$$
$$3x+4y=6$$

using matrices.

Program

A <- matrix(c(2,1,3,4),2,2,byrow=TRUE)

B <- matrix(c(5,6),2,1)

X <- solve(A)%*%B

cat("Solution:\n")
print(X)

Output

          [,1]
[1,]  2.800000
[2,] -0.600000

Concepts Demonstrated

• Inverse of matrix
• Matrix multiplication
• System of equations

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4. Image Brightness Adjustment

Problem

A grayscale image is represented as a matrix. Increase the brightness by 50 units.

Program

image <- matrix(c(
50,60,70,
80,90,100,
120,130,140),3,3,byrow=TRUE)

cat("Original Image\n")
print(image)

bright_image <- image + 50

cat("Brightened Image\n")
print(bright_image)

Output

Original Image

50  60  70
80  90 100
120 130 140

Brightened Image

100 110 120
130 140 150
170 180 190

Concepts Demonstrated

• Scalar operations
• Matrix arithmetic
• Image representation

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5. Distance Matrix Between Points

Problem

Given coordinates of points, compute the Euclidean distance between every pair of points.

Points:

P1=(1,2)
P2=(4,6)
P3=(7,3)

Program

points <- matrix(c(1,2,4,6,7,3), nrow=3, byrow=TRUE)

n <- nrow(points)

distance_matrix <- matrix(0,n,n)

for(i in 1:n)
{
  for(j in 1:n)
  {
    distance_matrix[i,j] <-
      sqrt((points[i,1]-points[j,1])^2 +
           (points[i,2]-points[j,2])^2)
  }
}

print(distance_matrix)

Output

         [,1]     [,2]     [,3]
[1,] 0.000000 5.000000 6.082763
[2,] 5.000000 0.000000 4.242641
[3,] 6.082763 4.242641 0.000000