Vector arithmetic (element-wise) in R Programming - Step-by-Step Execution

Concept Flow - Vector arithmetic (element-wise)

Start with two vectors

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Add/subtract/multiply/divide elements

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Perform operation element-wise

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Result: new vector with element-wise results

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End

This flow shows how two vectors are combined by doing the operation on each pair of elements one by one.

Execution Sample

R Programming

a <- c(2, 4, 6)
b <- c(1, 3, 5)
c <- a + b
print(c)

Adds two vectors element by element and prints the result.

Execution Table

Step	Operation	a[i]	b[i]	Result[i]	Explanation
1	Add	2	1	3	2 + 1 = 3
2	Add	4	3	7	4 + 3 = 7
3	Add	6	5	11	6 + 5 = 11
4	Print result	-	-	3 7 11	Final vector after element-wise addition

💡 All elements processed; vector addition complete.

Variable Tracker

Variable	Start	After 1	After 2	After 3	Final
a	c(2,4,6)	2	4	6	c(2,4,6)
b	c(1,3,5)	1	3	5	c(1,3,5)
c	empty	3	7	11	c(3,7,11)

Key Moments - 2 Insights

Why does R add vectors element by element instead of summing all elements?

R performs vector arithmetic element-wise by design, as shown in execution_table rows 1-3, where each pair of elements is added separately to produce a new vector.

What happens if vectors have different lengths?

If vectors differ in length, R recycles the shorter vector elements to match the longer one. This is not shown here but is important to avoid unexpected results.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of c[2] after the second step?

A 3

B 4

C 7

D 11

💡 Hint

Check the 'Result[i]' column in row 2 of execution_table.

At which step does the vector c get fully created?

A Step 3

B Step 1

C Step 4

D Step 2

💡 Hint

Look at the 'Operation' column and see when the full vector is printed.

If vector b was shorter, how would the addition behave?

A It would cause an error

B It would recycle elements of b to match a

C It would ignore extra elements in a

D It would add only the first element of b to all elements of a

💡 Hint

Recall the key_moments explanation about vector length differences.

Concept Snapshot

Vector arithmetic in R works element-wise.
Use +, -, *, / operators between vectors.
Each element in one vector combines with the corresponding element in the other.
If vectors differ in length, shorter vector elements recycle.
Result is a new vector of the same length as the longest input.

Full Transcript

This example shows how R adds two vectors element by element. Starting with vectors a and b, each element pair is added to form a new vector c. The execution table traces each addition step, showing the values combined and the result. The variable tracker shows how c builds up over time. Beginners often wonder why R does element-wise addition instead of summing all elements; this is because vector arithmetic is designed to work element-wise. Also, if vectors have different lengths, R recycles the shorter vector's elements to match the longer one. The visual quiz tests understanding of the step-by-step addition and behavior with different vector lengths.