Matrix creation in R Programming - Step-by-Step Execution

Concept Flow - Matrix creation

Start with vector of elements

↓

Call matrix() function

↓

Specify rows and columns

↓

Fill matrix by columns (default) or rows

↓

Matrix created and stored

Create a matrix by providing a vector of elements and specifying the number of rows and columns. The matrix fills by columns by default.

Execution Sample

R Programming

vec <- 1:6
mat <- matrix(vec, nrow=2, ncol=3)
print(mat)

Creates a 2-row, 3-column matrix from numbers 1 to 6 and prints it.

Execution Table

Step	Action	Vector Elements	Matrix Shape	Matrix Content
1	Create vector vec	1,2,3,4,5,6	-	-
2	Call matrix(vec, nrow=2, ncol=3)	1,2,3,4,5,6	2 rows, 3 cols	-
3	Fill matrix by columns	1,2,3,4,5,6	2x3	[1 3 5 2 4 6]
4	Print matrix	-	2x3	[,1] [,2] [,3] [1,] 1 3 5 [2,] 2 4 6

💡 Matrix created with 2 rows and 3 columns filled column-wise from vector elements.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
vec	-	c(1,2,3,4,5,6)	c(1,2,3,4,5,6)	c(1,2,3,4,5,6)	c(1,2,3,4,5,6)
mat	-	-	matrix(2,3) unfilled	matrix(2,3) filled column-wise	matrix(2,3) filled column-wise

Key Moments - 2 Insights

Why does the matrix fill by columns and not by rows?

By default, R's matrix() fills elements column-wise as shown in step 3 of the execution_table. To fill by rows, you must set byrow=TRUE.

What happens if the number of elements in the vector does not match rows*columns?

R recycles elements to fill the matrix. This is not shown here but is important to know for matrix creation.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the element at row 2, column 3 of the matrix?

A 6

B 5

C 3

D 4

💡 Hint

Check the matrix content column-wise filling in step 3 of execution_table.

At which step is the matrix shape defined?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at the 'Matrix Shape' column in execution_table.

If we add byrow=TRUE in matrix(), how would the matrix content change at step 3?

A Matrix fills diagonally

B Matrix fills row-wise: [1 2 3; 4 5 6]

C Matrix fills column-wise: [1 3 5; 2 4 6]

D Matrix remains empty

💡 Hint

Recall the default filling is column-wise; byrow=TRUE changes it to row-wise.

Concept Snapshot

matrix(data, nrow, ncol, byrow=FALSE)
- Creates a matrix from data vector
- nrow and ncol set dimensions
- byrow=FALSE fills columns first
- byrow=TRUE fills rows first
- Recycling if data length < nrow*ncol

Full Transcript

This visual execution shows how to create a matrix in R. First, a vector of elements is created. Then the matrix() function is called with the vector and specified rows and columns. By default, the matrix fills column-wise with the vector elements. The final matrix is printed showing the elements arranged in 2 rows and 3 columns. Key points include the default column-wise filling and the ability to change it with byrow=TRUE. The variable tracker shows how the vector and matrix variables change during execution.

Practice

1. What does the matrix() function in R primarily do?

easy

A. Creates a table of values arranged in rows and columns

B. Generates a list of random numbers

C. Sorts a vector in ascending order

D. Calculates the sum of all elements in a vector

Solution

1. Step 1: Understand the purpose of matrix()

   The matrix() function is designed to create a matrix, which is a table of values arranged in rows and columns.

2. Step 2: Compare with other options

   Options A, B, and C describe different functions or operations unrelated to matrix creation.

3. Final Answer:

   Creates a table of values arranged in rows and columns -> Option A

4. Quick Check:

   matrix() creates tables = D [OK]

Hint: matrix() makes tables with rows and columns [OK]

Common Mistakes:

• Confusing matrix() with functions that generate random numbers
• Thinking matrix() sorts data
• Assuming matrix() sums elements

2. Which of the following is the correct syntax to create a 2x3 matrix filled by rows with numbers 1 to 6 in R?

easy

A. matrix(1:6, nrow=3, ncol=2, byrow=TRUE)

B. matrix(1:6, nrow=2, ncol=3, byrow=TRUE)

C. matrix(1:6, nrow=2, ncol=3, byrow=FALSE)

D. matrix(1:6, nrow=3, ncol=2, byrow=FALSE)

Solution

1. Step 1: Identify matrix dimensions and filling order

   The question asks for a 2 rows by 3 columns matrix filled by rows with numbers 1 to 6.

2. Step 2: Match syntax to requirements

   matrix(1:6, nrow=2, ncol=3, byrow=TRUE) uses nrow=2, ncol=3, and byrow=TRUE, which matches the question exactly.

3. Final Answer:

   matrix(1:6, nrow=2, ncol=3, byrow=TRUE) -> Option B

4. Quick Check:

   2 rows, 3 cols, byrow=TRUE = A [OK]

Hint: Match nrow, ncol, and byrow exactly [OK]

Common Mistakes:

• Swapping nrow and ncol values
• Forgetting to set byrow=TRUE for row-wise filling
• Using byrow=FALSE when row-wise fill is needed

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

m <- matrix(1:6, nrow=2, ncol=3, byrow=FALSE)
print(m)

medium

A. [,1] [,2] [,3]
[1,] 1 4 2
[2,] 3 5 6

B. [[1, 3, 5], [2, 4, 6]]

C. [[1, 2, 3], [4, 5, 6]]

D. [,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6

Solution

1. Step 1: Understand matrix filling by columns

   With byrow=FALSE, the matrix fills column-wise: first column gets 1 and 2, second gets 3 and 4, third gets 5 and 6.

2. Step 2: Write matrix layout

   Row 1: 1, 3, 5
   Row 2: 2, 4, 6

3. Final Answer:

   [,1] [,2] [,3] [1,] 1 3 5 [2,] 2 4 6 -> Option D

4. Quick Check:

   byrow=FALSE fills columns = A [OK]

Hint: byrow=FALSE fills columns top to bottom [OK]

Common Mistakes:

• Assuming byrow=FALSE fills rows instead of columns
• Mixing up row and column indices in output
• Confusing output format with list notation

4. Identify the error in this R code that tries to create a 3x2 matrix:

matrix(1:6, nrow=3, ncol=2, byrow=TRUE, fill=TRUE)

medium

A. The argument 'fill' is not valid in matrix()

B. nrow and ncol values are swapped

C. byrow must be FALSE for this matrix size

D. 1:6 cannot fill a 3x2 matrix

Solution

1. Step 1: Check matrix() arguments

   The matrix() function does not have a fill argument; this causes an error.

2. Step 2: Validate other arguments

   nrow=3 and ncol=2 are valid, byrow=TRUE is allowed, and 1:6 perfectly fills a 3x2 matrix.

3. Final Answer:

   The argument 'fill' is not valid in matrix() -> Option A

4. Quick Check:

   Invalid argument 'fill' causes error = C [OK]

Hint: matrix() has no 'fill' argument [OK]

Common Mistakes:

• Assuming 'fill' is a valid argument
• Swapping nrow and ncol unnecessarily
• Thinking byrow must be FALSE for certain sizes

5. You want to create a 4x4 matrix in R where the numbers 1 to 16 fill the matrix by rows, but every even number should be replaced by 0. Which code correctly achieves this?

hard

A. matrix(ifelse((1:16) %% 2 == 0, 0, 1:16), nrow=4, ncol=4, byrow=FALSE)

B. matrix(ifelse((1:16) %% 2 == 1, 0, 1:16), nrow=4, ncol=4, byrow=TRUE)

C. matrix(ifelse((1:16) %% 2 == 0, 0, 1:16), nrow=4, ncol=4, byrow=TRUE)

D. matrix(ifelse((1:16) %% 2 == 1, 0, 1:16), nrow=4, ncol=4, byrow=FALSE)

Solution

1. Step 1: Replace even numbers with 0

   The expression ifelse((1:16) %% 2 == 0, 0, 1:16) replaces even numbers with 0 and keeps odd numbers as is.

2. Step 2: Create 4x4 matrix filled by rows

   Using nrow=4, ncol=4, and byrow=TRUE fills the matrix row-wise as required.

3. Final Answer:

   matrix(ifelse((1:16) %% 2 == 0, 0, 1:16), nrow=4, ncol=4, byrow=TRUE) -> Option C

4. Quick Check:

   Replace evens with 0, fill by rows = B [OK]

Hint: Use ifelse() and byrow=TRUE for row-wise conditional fill [OK]

Common Mistakes:

• Using byrow=FALSE when row-wise fill is needed
• Replacing odd numbers instead of even
• Not using ifelse() for conditional replacement