Special operators (%in%, %*%) in R Programming - Step-by-Step Execution

Concept Flow - Special operators (%in%, %*%)

Start

↓

Evaluate left operand

↓

Evaluate right operand

↓

%in%: Check if elements of left are in right

↓

%*%: Perform matrix multiplication

↓

Return result

↓

End

The special operators %in% and %*% take two inputs, evaluate them, then perform membership test or matrix multiplication, and return the result.

Execution Sample

R Programming

x <- c(1, 2, 3)
y <- c(2, 3, 4)
x %in% y
A <- matrix(1:4, 2, 2)
B <- matrix(5:8, 2, 2)
A %*% B

Check which elements of x are in y using %in%, then multiply matrices A and B using %*%.

Execution Table

Step	Expression	Evaluation	Result
1	x <- c(1, 2, 3)	Assign vector	x = (1, 2, 3)
2	y <- c(2, 3, 4)	Assign vector	y = (2, 3, 4)
3	x %in% y	Check each element of x in y	(FALSE, TRUE, TRUE)
4	A <- matrix(1:4, 2, 2)	Assign matrix	A = [[1, 3], [2, 4]]
5	B <- matrix(5:8, 2, 2)	Assign matrix	B = [[5, 7], [6, 8]]
6	A %*% B	Multiply matrices	[[17, 23], [39, 53]]

💡 All expressions evaluated, results returned for %in% and %*%.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 4	After Step 5	Final
x	undefined	(1, 2, 3)	(1, 2, 3)	(1, 2, 3)	(1, 2, 3)	(1, 2, 3)
y	undefined	undefined	(2, 3, 4)	(2, 3, 4)	(2, 3, 4)	(2, 3, 4)
A	undefined	undefined	undefined	[[1, 3], [2, 4]]	[[1, 3], [2, 4]]	[[1, 3], [2, 4]]
B	undefined	undefined	undefined	undefined	[[5, 7], [6, 8]]	[[5, 7], [6, 8]]

Key Moments - 2 Insights

Why does x %in% y return a logical vector instead of a single TRUE or FALSE?

Because %in% checks each element of x individually against y, returning TRUE or FALSE for each element as shown in step 3 of the execution_table.

How does %*% differ from the usual * operator in R?

The %*% operator performs matrix multiplication, combining rows and columns, unlike * which does element-wise multiplication. This is shown in step 6 where matrices A and B are multiplied.

Visual Quiz - 3 Questions

Look at the execution_table at step 3. What is the result of x %in% y?

A (FALSE, TRUE, TRUE)

B (TRUE, TRUE, TRUE)

C (TRUE, FALSE, FALSE)

D (FALSE, FALSE, FALSE)

💡 Hint

Check the 'Result' column at step 3 in the execution_table.

At which step does matrix multiplication happen?

A Step 4

B Step 5

C Step 6

D Step 3

💡 Hint

Look for the step where %*% operator is used in the 'Expression' column.

If we change y to c(1, 4, 5), what would be the result of x %in% y at step 3?

A (TRUE, FALSE, TRUE)

B (TRUE, FALSE, FALSE)

C (FALSE, TRUE, TRUE)

D (FALSE, FALSE, FALSE)

💡 Hint

Compare elements of x with new y values and check membership.

Concept Snapshot

Special operators in R:
- %in% checks if elements of left vector are in right vector, returns logical vector.
- %*% performs matrix multiplication between two matrices.
- Use %in% for membership tests, %*% for linear algebra.
- Both require two operands and return a result based on their operation.

Full Transcript

This visual execution shows how R's special operators %in% and %*% work. First, vectors x and y are assigned. Then x %in% y checks each element of x to see if it is in y, returning a logical vector. Next, matrices A and B are assigned. The operator %*% multiplies these matrices using matrix multiplication rules, producing a new matrix. Variables are tracked through each step to show their values. Key moments clarify why %in% returns a vector and how %*% differs from element-wise multiplication. The quiz tests understanding of results and operator behavior.

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