Special operators (%in%, %*%) in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the %in% operator do in R?

The %in% operator checks if elements of one vector are present in another vector. It returns a logical vector of TRUE or FALSE values.

beginner

How does the %*% operator work in R?

The %*% operator performs matrix multiplication between two matrices or vectors, following the rules of linear algebra.

beginner

Example: What is the result of c(1, 2, 3) %in% c(2, 3, 4)?

The result is a logical vector: FALSE TRUE TRUE. It shows which elements of the first vector are found in the second.

intermediate

Example: What is the output of matrix(c(1,2,3,4), nrow=2) %*% matrix(c(5,6,7,8), nrow=2)?

The output is a 2x2 matrix: [,1] [,2] [1,] 19 22 [2,] 43 50 This is the result of multiplying the two matrices using matrix multiplication rules.

intermediate

Can %in% be used with data frames or lists?

Yes, %in% can be used to check if elements exist in vectors extracted from data frames or lists, but it works element-wise on vectors, not directly on data frames.

What does the expression '3 %in% c(1, 2, 3, 4)' return in R?

A TRUE

B FALSE

C 3

D Error

3 is present in the vector c(1, 2, 3, 4), so %in% returns TRUE.

Which operator is used for matrix multiplication in R?

A *

B %*%

C %in%

D %%

The %*% operator performs matrix multiplication in R.

What is the output type of 'c(1,2,3) %in% c(2,3,4)'?

A Numeric vector

B Matrix

C Logical vector

D Character vector

%in% returns a logical vector indicating presence or absence.

If A is a 2x3 matrix and B is a 3x2 matrix, what does A %*% B produce?

A Error

B A 3x3 matrix

C A 2x3 matrix

D A 2x2 matrix

Matrix multiplication of 2x3 and 3x2 matrices results in a 2x2 matrix.

Can %in% be used to check if a value is in a list directly?

A No, it only works on vectors

B Yes, it works directly on lists

C Yes, but only for numeric lists

D No, it only works on matrices

%in% works element-wise on vectors, not directly on lists.

Explain how the %in% operator works and give a simple example.

Think about checking if items are inside a shopping list.

Describe the purpose of the %*% operator and what kind of data it works with.

Imagine multiplying two tables of numbers to get a new table.

Practice

1. What does the %in% operator do in R?

easy

A. Calculates the sum of two vectors

B. Performs element-wise multiplication of two vectors

C. Performs matrix multiplication

D. Checks if elements of one vector are present in another vector

Solution

1. Step 1: Understand the purpose of %in%

   The %in% operator is used to check membership, meaning it tests if elements of one vector exist in another.

2. Step 2: Compare with other operations

   Other options describe arithmetic or matrix operations, which are not the function of %in%.

3. Final Answer:

   Checks if elements of one vector are present in another vector -> Option D

4. Quick Check:

   %in% = membership check [OK]

Hint: Remember: %in% means 'is in' for membership [OK]

Common Mistakes:

• Confusing %in% with arithmetic operators
• Thinking %in% does matrix multiplication
• Assuming %in% returns numeric results

2. Which of the following is the correct syntax for matrix multiplication in R?

easy

A. A * B

B. A %*% B

C. A %in% B

D. A + B

Solution

1. Step 1: Identify matrix multiplication operator

   In R, matrix multiplication is done using %*%, so A %*% B is correct syntax.

2. Step 2: Differentiate from other operators

   * is element-wise multiplication, %in% is membership, and + is addition.

3. Final Answer:

   A %*% B -> Option B

4. Quick Check:

   Matrix multiply = %*% [OK]

Hint: Use %*% for matrix multiply, * for element-wise [OK]

Common Mistakes:

• Using * instead of %*% for matrix multiplication
• Confusing %in% with multiplication
• Using + for multiplication

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

x <- c(3, 1, 5)
y <- c(3, 4, 5, 6)
x %in% y

medium

A. [TRUE, FALSE, TRUE]

B. [FALSE, TRUE, FALSE]

C. [TRUE, TRUE, TRUE]

D. [FALSE, FALSE, FALSE]

Solution

1. Step 1: Check each element of x in y

   3 is in y, so TRUE; 1 is not in y, so FALSE; 5 is in y, TRUE.

2. Step 2: Form the logical vector

   The result is [TRUE, FALSE, TRUE].

3. Final Answer:

   [TRUE, FALSE, TRUE] -> Option A

4. Quick Check:

   %in% returns logical vector [OK]

Hint: Check each element presence one by one [OK]

Common Mistakes:

• Mixing order of TRUE/FALSE in output
• Assuming %in% returns indices
• Confusing %in% with element-wise comparison

4. Identify the error in the following R code:

A <- matrix(c(1,2,3,4), nrow=2)
B <- matrix(c(5,6,7,8), nrow=2)
C <- A *%* B

medium

A. Matrices A and B have incompatible dimensions

B. Missing library for matrix multiplication

C. Incorrect operator *%* used for matrix multiplication

D. Matrix A is not defined properly

Solution

1. Step 1: Check operator syntax

   The operator *%* is invalid in R; correct operator is %*%.

2. Step 2: Verify matrix dimensions and definitions

   Both matrices are 2x2, so dimensions are compatible and matrices are defined correctly.

3. Final Answer:

   Incorrect operator *%* used for matrix multiplication -> Option C

4. Quick Check:

   Matrix multiply operator is %*% [OK]

Hint: Use %*% exactly for matrix multiplication [OK]

Common Mistakes:

• Typing operators in wrong order
• Assuming *%* is valid
• Confusing element-wise * with matrix multiply

5. Given two matrices:

M1 <- matrix(c(1, 0, 2, 3), nrow=2)
M2 <- matrix(c(4, 1, 0, 2), nrow=2)

Which R expression correctly computes the matrix product and then checks if the number 5 is in the resulting matrix?

hard

A. 5 %in% (M1 %*% M2)

B. M1 *%*% M2 %in% 5

C. M1 %in% 5 %*% M2

D. M1 %*% M2 == 5

Solution

1. Step 1: Perform matrix multiplication correctly

   Use %*% to multiply M1 and M2: M1 %*% M2.

2. Step 2: Check membership of 5 in the product matrix

   Use %in% to check if 5 is present in the resulting matrix: 5 %in% (M1 %*% M2).

3. Final Answer:

   5 %in% (M1 %*% M2) -> Option A

4. Quick Check:

   Matrix multiply then membership check = 5 %in% (M1 %*% M2) [OK]

Hint: Chain %*% then %in% with parentheses [OK]

Common Mistakes:

• Using wrong operator order
• Typing *%*% instead of %*%
• Using == instead of %in% for membership