Vector arithmetic (element-wise) in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is vector arithmetic (element-wise) in R?

It means performing operations like addition, subtraction, multiplication, or division on each pair of elements from two vectors of the same length, one by one.

intermediate

How does R handle vector addition when vectors have different lengths?

R recycles the shorter vector to match the length of the longer one, repeating its elements until lengths match, but it gives a warning if the longer vector's length is not a multiple of the shorter one.

beginner

What will be the result of c(1, 2, 3) + c(4, 5, 6) in R?

A new vector where each element is the sum of elements at the same position: c(5, 7, 9).

beginner

Explain element-wise multiplication of vectors in R with an example.

Element-wise multiplication multiplies each element of one vector by the corresponding element of another vector. For example, c(2, 3, 4) * c(5, 6, 7) results in c(10, 18, 28).

intermediate

What happens if you perform element-wise division with vectors of different lengths in R?

R recycles the shorter vector to match the longer one and divides elements pairwise, but warns if lengths are not multiples. For example, c(10, 20, 30, 40) / c(2, 5) results in c(5, 4, 15, 8).

What does element-wise addition of vectors mean in R?

A Adding the first element of one vector to all elements of the other

B Adding all elements of both vectors together

C Adding each element of one vector to the corresponding element of another vector

D Concatenating two vectors

Element-wise addition adds elements at the same positions in two vectors.

What will R do if you add vectors of different lengths?

A Ignore the shorter vector

B Return an error and stop

C Only add elements up to the length of the shorter vector

D Recycle the shorter vector to match the longer one

R recycles the shorter vector elements to match the longer vector length.

What is the result of c(3, 6, 9) * c(2, 4, 6) in R?

A c(6, 24, 54)

B c(1, 2, 3)

C c(5, 10, 15)

D c(3, 6, 9, 2, 4, 6)

Element-wise multiplication multiplies each pair: 3*2=6, 6*4=24, 9*6=54.

If you divide c(8, 16, 24) by c(2, 4), what will happen?

A Error due to different lengths

B Result c(4, 4, 12) with a warning

C Result c(4, 4, 6) with a warning

D Result c(4, 4, 12) without warning

Shorter vector c(2,4) is recycled to c(2,4,2). Division: 8/2=4, 16/4=4, 24/2=12 with a warning.

Which operator is used for element-wise subtraction in R?

A -

B +

C *

D /

The minus sign (-) subtracts elements pairwise in vectors.

Describe how R performs element-wise arithmetic operations on vectors and what happens when vectors have different lengths.

Think about how R matches elements by position and repeats shorter vectors.

Give examples of element-wise addition, multiplication, and division of vectors in R, explaining the results.

Use simple vectors like c(1,2,3) and c(4,5,6) to illustrate.

Practice

1.

What happens when you add two vectors of the same length in R, like c(1, 2, 3) + c(4, 5, 6)?

easy

A. The vectors are concatenated into one longer vector.

B. Only the first elements are added, the rest are ignored.

C. Each element in the first vector is added to the corresponding element in the second vector.

D. An error occurs because vectors cannot be added.

Solution

1. Step 1: Understand element-wise addition

   In R, adding two vectors of the same length adds each element from the first vector to the matching element in the second vector.

2. Step 2: Apply addition to given vectors

   Adding c(1, 2, 3) and c(4, 5, 6) results in c(1+4, 2+5, 3+6) which is c(5, 7, 9).

3. Final Answer:

   Each element in the first vector is added to the corresponding element in the second vector. -> Option C

4. Quick Check:

   Element-wise addition = Each element in the first vector is added to the corresponding element in the second vector. [OK]

Hint: Add vectors element by element when lengths match [OK]

Common Mistakes:

• Thinking vectors concatenate instead of adding
• Assuming only first elements add
• Expecting an error for vector addition

2.

Which of the following is the correct syntax to subtract two vectors a and b element-wise in R?

easy

A. subtract_vectors(a, b)

B. subtract(a, b)

C. a %minus% b

D. a - b

Solution

1. Step 1: Recall vector subtraction syntax in R

   In R, element-wise subtraction of vectors uses the minus operator - directly between vectors.

2. Step 2: Verify given options

   Only a - b is valid R syntax for element-wise subtraction. The other options are not built-in R functions or operators.

3. Final Answer:

   a - b -> Option D

4. Quick Check:

   Use - operator for vector subtraction [OK]

Hint: Use '-' operator directly between vectors [OK]

Common Mistakes:

• Using non-existent functions like subtract()
• Trying special operators like %minus%
• Confusing subtraction with other functions

3.

What is the output of the following R code?

v1 <- c(2, 4, 6)
v2 <- c(1, 3, 5)
result <- v1 * v2
print(result)

medium

A. [1] 2 4 6 1 3 5

B. [1] 2 12 30

C. [1] 2 7 11

D. [1] 3 7 11

Solution

1. Step 1: Understand element-wise multiplication

   In R, multiplying two vectors multiplies each element of the first vector by the corresponding element of the second vector.

2. Step 2: Calculate each product

   Multiply elements: 2*1=2, 4*3=12, 6*5=30. So the result is c(2, 12, 30).

3. Final Answer:

   [1] 2 12 30 -> Option B

4. Quick Check:

   Element-wise multiplication = [1] 2 12 30 [OK]

Hint: Multiply vectors element by element for correct output [OK]

Common Mistakes:

• Adding instead of multiplying
• Concatenating vectors instead of multiplying
• Getting sums instead of products

4.

Consider this R code snippet:

v1 <- c(1, 2, 3)
v2 <- c(4, 5)
result <- v1 + v2
print(result)

What is the issue with this code?

medium

A. Vectors have different lengths causing recycling warning.

B. Syntax error due to missing operator.

C. Result will be NULL because vectors differ in length.

D. No issue; code runs correctly without warnings.

Solution

1. Step 1: Check vector lengths

   Vector v1 has length 3, v2 has length 2. They differ in length.

2. Step 2: Understand recycling in R

   R recycles the shorter vector to match the longer one but gives a warning if lengths are not multiples. Here, 3 is not a multiple of 2, so a warning occurs.

3. Final Answer:

   Vectors have different lengths causing recycling warning. -> Option A

4. Quick Check:

   Unequal vector lengths cause recycling warning [OK]

Hint: Vectors must be same length or multiples to avoid warnings [OK]

Common Mistakes:

• Ignoring recycling warnings
• Expecting syntax errors for length mismatch
• Assuming result is NULL when lengths differ

5.

You have two vectors representing daily sales for two stores:
store1 <- c(10, 20, 30, 40)
store2 <- c(5, 15, 25, 35)
How do you calculate the total sales per day for both stores combined using vector arithmetic?

hard

A. total_sales <- store1 + store2

B. total_sales <- store1 * store2

C. total_sales <- store1 - store2

D. total_sales <- c(store1, store2)

Solution

1. Step 1: Understand the goal

   We want total sales per day, so we add sales from both stores for each day.

2. Step 2: Use element-wise addition

   Adding store1 and store2 element-wise sums daily sales: c(10+5, 20+15, 30+25, 40+35) = c(15, 35, 55, 75).

3. Final Answer:

   total_sales <- store1 + store2 -> Option A

4. Quick Check:

   Add vectors element-wise for daily totals [OK]

Hint: Add vectors to combine daily sales totals [OK]

Common Mistakes:

• Multiplying instead of adding sales
• Subtracting sales mistakenly
• Concatenating vectors instead of adding