Matrix dimensions in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this R code for matrix dimensions?

Consider the following R code that creates a matrix and then checks its dimensions. What will be printed?

R Programming

m <- matrix(1:12, nrow=3, ncol=4)
dim(m)

A [1] 12

B [1] 3 4

C [1] 4 3

D NULL

💡 Hint

The dim() function returns the number of rows and columns in that order.

The matrix m has 3 rows and 4 columns, so dim(m) returns a vector with 3 and 4.

❓ Predict Output

intermediate

What does this code print for matrix dimensions after transpose?

Given the matrix m and its transpose t(m), what will dim(t(m)) return?

R Programming

m <- matrix(1:6, nrow=2, ncol=3)
dim(t(m))

A [1] 3 2

B [1] 2 3

C [1] 6

D NULL

💡 Hint

Transpose swaps rows and columns.

Original matrix has 2 rows and 3 columns, transpose swaps them to 3 rows and 2 columns.

❓ Predict Output

advanced

What is the output of dim() on a vector converted to matrix?

What will be the output of dim() when applied to a vector converted to a matrix with one column?

R Programming

v <- 1:5
m <- matrix(v, ncol=1)
dim(m)

A [1] 1 5

B [1] 5

C [1] 5 1

D NULL

💡 Hint

Matrix with ncol=1 means one column and rows equal to length of vector.

The matrix has 5 rows and 1 column, so dim returns c(5,1).

❓ Predict Output

advanced

What error or output occurs when dim() is applied to a list?

What happens when you run dim() on a list in R?

R Programming

lst <- list(a=1, b=2)
dim(lst)

A [1] 1 2

B Error in dim(lst) : 'dim' applied to non-array

C [1] 2

D NULL

💡 Hint

Lists do not have dimensions like matrices or arrays.

dim() returns NULL for lists because they do not have dimensions.

🧠 Conceptual

expert

How many elements are in a matrix with dim attribute c(4,5)?

If a matrix in R has dimensions 4 rows and 5 columns, how many elements does it contain?

A 20

B 5

C 10

D 9

💡 Hint

Multiply rows by columns to get total elements.

A matrix with 4 rows and 5 columns has 4*5 = 20 elements.

Practice

1. What does the dim() function return when used on a matrix in R?

easy

A. The first element of the matrix

B. The sum of all elements in the matrix

C. A vector with the number of rows and columns

D. The matrix converted to a vector

Solution

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

   The dim() function in R returns the dimensions of an object, typically a matrix or array.

2. Step 2: What does it return for a matrix?

   For a matrix, dim() returns a vector of length two: the number of rows and the number of columns.

3. Final Answer:

   A vector with the number of rows and columns -> Option C

4. Quick Check:

   dim(matrix) = c(rows, columns) [OK]

Hint: Remember dim() gives rows and columns together [OK]

Common Mistakes:

• Thinking dim() returns sum of elements
• Confusing dim() with length()
• Expecting dim() to return matrix elements

2. Which of the following is the correct way to create a 3x2 matrix in R?

easy

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

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

C. matrix(1:6, rows=3, cols=2)

D. matrix(1:6, 3, 2, byrow=TRUE)

Solution

1. Step 1: Check the matrix function parameters

   The matrix() function uses nrow and ncol to specify rows and columns.

2. Step 2: Identify correct parameter names and values

   matrix(1:6, nrow=3, ncol=2) uses nrow=3 and ncol=2, which correctly creates a 3-row, 2-column matrix.

3. Final Answer:

   matrix(1:6, nrow=3, ncol=2) -> Option A

4. Quick Check:

   Use nrow and ncol to set dimensions [OK]

Hint: Use nrow and ncol to set matrix size [OK]

Common Mistakes:

• Using wrong parameter names like rows or cols
• Swapping nrow and ncol values
• Omitting parameter names causing confusion

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

m <- matrix(1:12, nrow=3, ncol=4)
dim(m)

medium

A. [1] 12

B. [1] 4 3

C. [1] 3

D. [1] 3 4

Solution

1. Step 1: Understand matrix creation

   The matrix m is created with 3 rows and 4 columns using nrow=3 and ncol=4.

2. Step 2: Check the output of dim(m)

   The dim() function returns a vector with the number of rows and columns, so it returns 3 4.

3. Final Answer:

   [1] 3 4 -> Option D

4. Quick Check:

   dim(m) = c(3, 4) [OK]

Hint: dim() returns rows then columns vector [OK]

Common Mistakes:

• Confusing order of rows and columns
• Expecting dim() to return total elements
• Misreading output as a single number

4. Identify the error in this R code snippet:

m <- matrix(1:9, nrow=3, ncol=3)
dim(m) <- c(2, 5)

medium

A. The code is correct and runs without error

B. You cannot assign dimensions that don't match the number of elements

C. dim() cannot be used on matrices

D. The matrix function is missing the byrow argument

Solution

1. Step 1: Check the original matrix size

   The matrix m has 9 elements (3 rows x 3 columns).

2. Step 2: Analyze the dimension assignment

   Assigning dim(m) <- c(2, 5) tries to reshape m to 2 rows and 5 columns, which requires 10 elements, not 9.

3. Final Answer:

   You cannot assign dimensions that don't match the number of elements -> Option B

4. Quick Check:

   New dims must match total elements [OK]

Hint: New dimensions must multiply to total elements [OK]

Common Mistakes:

• Ignoring element count mismatch
• Thinking dim() cannot be assigned
• Assuming byrow affects dimension assignment

5. You have a matrix m with dimensions 4x5. You want to reshape it into a matrix with 5 rows. Which of the following commands correctly changes the dimensions without losing data?

hard

A. dim(m) <- c(5, 4)

B. dim(m) <- c(5, 5)

C. dim(m) <- c(5, 3)

D. dim(m) <- c(5, 2)

Solution

1. Step 1: Calculate total elements in original matrix

   The original matrix has 4 rows x 5 columns = 20 elements.

2. Step 2: Check which new dimension matches total elements

   dim(m) <- c(5, 4) sets dimensions to 5 rows and 4 columns, which is 20 elements, matching original size.

3. Step 3: Verify other options

   Options B, C, and D have total elements 25, 15, and 10 respectively, which do not match 20, causing errors or data loss.

4. Final Answer:

   dim(m) <- c(5, 4) -> Option A

5. Quick Check:

   New dims must multiply to 20 [OK]

Hint: New rows x new cols = total elements [OK]

Common Mistakes:

• Choosing dimensions that don't match total elements
• Swapping rows and columns incorrectly
• Forgetting to check total element count