Matrix arithmetic in R Programming - Mini Project: Build & Apply

Matrix arithmetic

📖 Scenario: Imagine you work in a small company that tracks sales data in tables. Each table is a matrix where rows are products and columns are months. You want to do some basic math with these sales tables.

🎯 Goal: You will create two sales matrices, set a multiplier for a sales increase, multiply the matrices, and then print the result.

📋 What You'll Learn

Create two matrices with exact values

Create a multiplier variable

Multiply matrices using matrix multiplication

Print the resulting matrix

💡 Why This Matters

🌍 Real World

Matrix arithmetic is useful in business for analyzing sales data, financial modeling, and scientific calculations.

💼 Career

Many jobs in data analysis, finance, and engineering require working with matrices and performing matrix operations.

1

Create two sales matrices

Create a matrix called sales1 with values 1, 2, 3, 4, 5, 6 arranged in 2 rows and 3 columns, and another matrix called sales2 with values 7, 8, 9, 10, 11, 12 arranged in 3 rows and 2 columns.

R Programming

# Create sales1 and sales2 matrices with given values and dimensions
# Your code here

Hint

Use the matrix() function with c() to combine values, and specify nrow and ncol.

2

Set a sales multiplier

Create a variable called multiplier and set it to 2 to represent doubling sales.

R Programming

sales1 <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3)
sales2 <- matrix(c(7, 8, 9, 10, 11, 12), nrow = 3, ncol = 2)
# Create multiplier variable and set it to 2
# Your code here

Hint

Just assign the number 2 to the variable multiplier.

3

Multiply matrices with multiplier

Create a new matrix called result by multiplying sales1 and sales2 using matrix multiplication, then multiply the result by multiplier.

R Programming

sales1 <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3)
sales2 <- matrix(c(7, 8, 9, 10, 11, 12), nrow = 3, ncol = 2)
multiplier <- 2
# Multiply sales1 and sales2 using %*%, then multiply by multiplier and store in result
# Your code here

Hint

Use %*% for matrix multiplication and multiply the whole result by multiplier.

4

Print the result matrix

Print the matrix result to display the final sales after multiplication.

R Programming

sales1 <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3)
sales2 <- matrix(c(7, 8, 9, 10, 11, 12), nrow = 3, ncol = 2)
multiplier <- 2
result <- multiplier * (sales1 %*% sales2)
# Print the result matrix
# Your code here

Hint

Use the print() function to show the matrix result.

Practice

1. In R, what does the operator %*% do when applied between two matrices?

easy

A. Performs matrix multiplication following linear algebra rules

B. Adds the two matrices element-wise

C. Subtracts the second matrix from the first element-wise

D. Multiplies the two matrices element-wise

Solution

1. Step 1: Understand matrix operators in R

   In R, + and - perform element-wise addition and subtraction respectively, while %*% is used for matrix multiplication.

2. Step 2: Identify the role of %*%

   The operator %*% multiplies matrices according to linear algebra rules, not element-wise.

3. Final Answer:

   Performs matrix multiplication following linear algebra rules -> Option A

4. Quick Check:

   %*% = matrix multiplication [OK]

Hint: Remember: %*% means matrix multiplication, not element-wise [OK]

Common Mistakes:

• Confusing %*% with element-wise multiplication
• Thinking + or - does matrix multiplication
• Using * for matrix multiplication

2. Which of the following is the correct way to create a 2x2 matrix with values 1, 2, 3, 4 in R?

easy

A. matrix(1, 2, 3, 4, 2, 2)

B. matrix(1, 2, 3, 4, nrow=2, ncol=2)

C. matrix(c(1, 2, 3, 4), rows=2, cols=2)

D. matrix(c(1, 2, 3, 4), nrow=2, ncol=2)

Solution

1. Step 1: Recall matrix creation syntax in R

   The function matrix() takes a vector of values and parameters nrow and ncol to specify dimensions.

2. Step 2: Check each option

   matrix(c(1, 2, 3, 4), nrow=2, ncol=2) correctly uses c(1, 2, 3, 4) and named arguments nrow=2, ncol=2. matrix(1, 2, 3, 4, nrow=2, ncol=2) has wrong argument format. matrix(c(1, 2, 3, 4), rows=2, cols=2) uses invalid argument names. matrix(1, 2, 3, 4, 2, 2) uses positional arguments without the vector wrapper.

3. Final Answer:

   matrix(c(1, 2, 3, 4), nrow=2, ncol=2) -> Option D

4. Quick Check:

   Use c() vector and nrow, ncol named args [OK]

Hint: Always wrap values in c() and name nrow, ncol [OK]

Common Mistakes:

• Not using c() to combine values
• Using wrong argument names like rows or cols
• Passing values without vector wrapper

3. What is the output of the following R code?

m1 <- matrix(c(1, 2, 3, 4), nrow=2, ncol=2, byrow=TRUE)
m2 <- matrix(c(5, 6, 7, 8), nrow=2, ncol=2, byrow=TRUE)
m3 <- m1 + m2
print(m3)

medium

A. [1 2; 3 4]

B. Error: non-conformable arrays

C. [6 8; 10 12]

D. [5 6; 7 8]

Solution

1. Step 1: Understand element-wise addition

   Using + between matrices adds corresponding elements: (1+5), (2+6), (3+7), (4+8).

2. Step 2: Calculate each element

   Results: 6, 8, 10, 12 arranged in 2x2 matrix.

3. Final Answer:

   [6 8; 10 12] -> Option C

4. Quick Check:

   Element-wise addition = sum of each element pair [OK]

Hint: Use + for element-wise addition, add each element pair [OK]

Common Mistakes:

• Expecting matrix multiplication instead of addition
• Confusing matrix dimensions causing errors
• Misreading matrix layout in output

4. Consider this R code snippet:

m1 <- matrix(c(1, 2, 3, 4), nrow=2)
m2 <- matrix(c(5, 6, 7), nrow=3)
m3 <- m1 %*% m2
print(m3)

What is the problem with this code?

medium

A. The matrices have incompatible dimensions for multiplication

B. The matrix m1 is not square

C. The operator %*% is invalid for matrices

D. The matrix m2 has missing values

Solution

1. Step 1: Check matrix dimensions

   m1 is 2x2, m2 is 3x1 (since 3 values and nrow=3). For multiplication, columns of m1 (2) must equal rows of m2 (3).

2. Step 2: Identify dimension mismatch

   2 != 3, so multiplication is not possible, causing an error.

3. Final Answer:

   The matrices have incompatible dimensions for multiplication -> Option A

4. Quick Check:

   Matrix multiplication needs matching inner dimensions [OK]

Hint: Check if m1 columns = m2 rows before multiplying [OK]

Common Mistakes:

• Assuming any matrices can be multiplied
• Ignoring dimension mismatch errors
• Thinking %*% works element-wise

5. You have two matrices in R:

m1 <- matrix(c(1, 0, 2, -1), nrow=2)
m2 <- matrix(c(3, 1, 4, 2), nrow=2)

You want to compute the matrix product m1 %*% m2 and then subtract the identity matrix of size 2. Which code correctly does this?

hard

A. m3 <- m1 * m2 - diag(2)

B. m3 <- m1 %*% m2 - diag(2)

C. m3 <- m1 %*% m2 - matrix(1, 2, 2)

D. m3 <- m1 %*% m2 - identity(2)

Solution

1. Step 1: Compute matrix multiplication

   Use %*% to multiply m1 and m2 correctly.

2. Step 2: Subtract identity matrix

   Use diag(2) to create a 2x2 identity matrix and subtract it from the product.

3. Final Answer:

   m3 <- m1 %*% m2 - diag(2) -> Option B

4. Quick Check:

   Use diag() for identity matrix in subtraction [OK]

Hint: Use diag(n) for identity matrix, %*% for multiplication [OK]

Common Mistakes:

• Using * instead of %*% for multiplication
• Using matrix(1,2,2) which is all ones, not identity
• Using identity() which is not an R base function