Matrix arithmetic in R Programming - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 2x2 matrix with values 1 to 4.

R Programming

mat <- matrix(1:4, nrow = [1], ncol = 2)

Drag options to blanks, or click blank then click option'

A1

B3

C2

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong number of rows like 3 or 4.

Confusing rows and columns.

The matrix has 2 rows and 2 columns, so nrow = 2 is correct.

2fill in blank

medium

Complete the code to add two matrices A and B.

R Programming

result <- [1] + B

Drag options to blanks, or click blank then click option'

AA

BB

Cmatrix

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum which sums all elements instead of element-wise addition.

Using matrix keyword incorrectly.

To add two matrices, use the + operator between them. Here, A + B.

3fill in blank

hard

Fix the error in the code to multiply matrices X and Y.

R Programming

product <- X [1] Y

Drag options to blanks, or click blank then click option'

A*

B%*%

C%

D%%

Attempts:

3 left

💡 Hint

Common Mistakes

Using * which does element-wise multiplication.

Using modulo operators like %% or %.

Matrix multiplication in R uses the operator %*%, not *.

4fill in blank

hard

Fill both blanks to create a matrix M with 3 rows and 4 columns filled by row.

R Programming

M <- matrix(1:12, nrow = [1], ncol = [2], byrow = TRUE)

Drag options to blanks, or click blank then click option'

A3

B4

CFALSE

DTRUE

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping rows and columns.

Setting byrow to FALSE by mistake.

The matrix has 3 rows and 4 columns, so nrow = 3 and ncol = 4.

5fill in blank

hard

Fill all three blanks to create a named matrix mat with row and column names.

R Programming

mat <- matrix(1:6, nrow = [1], ncol = [2], dimnames = list([3], c("A", "B")))

Drag options to blanks, or click blank then click option'

A2

B3

Cc("Row1", "Row2", "Row3")

Dc("Row1", "Row2")

Attempts:

3 left

💡 Hint

Common Mistakes

Mismatching row names length with number of rows.

Swapping rows and columns counts.

The matrix has 3 rows and 2 columns, so nrow = 3 and ncol = 2. The row names vector must match the number of rows, so c("Row1", "Row2", "Row3") is correct.

Practice

1. In R, what does the operator %*% do when applied between two matrices?

easy

A. Performs matrix multiplication following linear algebra rules

B. Adds the two matrices element-wise

C. Subtracts the second matrix from the first element-wise

D. Multiplies the two matrices element-wise

Solution

1. Step 1: Understand matrix operators in R

   In R, + and - perform element-wise addition and subtraction respectively, while %*% is used for matrix multiplication.

2. Step 2: Identify the role of %*%

   The operator %*% multiplies matrices according to linear algebra rules, not element-wise.

3. Final Answer:

   Performs matrix multiplication following linear algebra rules -> Option A

4. Quick Check:

   %*% = matrix multiplication [OK]

Hint: Remember: %*% means matrix multiplication, not element-wise [OK]

Common Mistakes:

• Confusing %*% with element-wise multiplication
• Thinking + or - does matrix multiplication
• Using * for matrix multiplication

2. Which of the following is the correct way to create a 2x2 matrix with values 1, 2, 3, 4 in R?

easy

A. matrix(1, 2, 3, 4, 2, 2)

B. matrix(1, 2, 3, 4, nrow=2, ncol=2)

C. matrix(c(1, 2, 3, 4), rows=2, cols=2)

D. matrix(c(1, 2, 3, 4), nrow=2, ncol=2)

Solution

1. Step 1: Recall matrix creation syntax in R

   The function matrix() takes a vector of values and parameters nrow and ncol to specify dimensions.

2. Step 2: Check each option

   matrix(c(1, 2, 3, 4), nrow=2, ncol=2) correctly uses c(1, 2, 3, 4) and named arguments nrow=2, ncol=2. matrix(1, 2, 3, 4, nrow=2, ncol=2) has wrong argument format. matrix(c(1, 2, 3, 4), rows=2, cols=2) uses invalid argument names. matrix(1, 2, 3, 4, 2, 2) uses positional arguments without the vector wrapper.

3. Final Answer:

   matrix(c(1, 2, 3, 4), nrow=2, ncol=2) -> Option D

4. Quick Check:

   Use c() vector and nrow, ncol named args [OK]

Hint: Always wrap values in c() and name nrow, ncol [OK]

Common Mistakes:

• Not using c() to combine values
• Using wrong argument names like rows or cols
• Passing values without vector wrapper

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

m1 <- matrix(c(1, 2, 3, 4), nrow=2, ncol=2, byrow=TRUE)
m2 <- matrix(c(5, 6, 7, 8), nrow=2, ncol=2, byrow=TRUE)
m3 <- m1 + m2
print(m3)

medium

A. [1 2; 3 4]

B. Error: non-conformable arrays

C. [6 8; 10 12]

D. [5 6; 7 8]

Solution

1. Step 1: Understand element-wise addition

   Using + between matrices adds corresponding elements: (1+5), (2+6), (3+7), (4+8).

2. Step 2: Calculate each element

   Results: 6, 8, 10, 12 arranged in 2x2 matrix.

3. Final Answer:

   [6 8; 10 12] -> Option C

4. Quick Check:

   Element-wise addition = sum of each element pair [OK]

Hint: Use + for element-wise addition, add each element pair [OK]

Common Mistakes:

• Expecting matrix multiplication instead of addition
• Confusing matrix dimensions causing errors
• Misreading matrix layout in output

4. Consider this R code snippet:

m1 <- matrix(c(1, 2, 3, 4), nrow=2)
m2 <- matrix(c(5, 6, 7), nrow=3)
m3 <- m1 %*% m2
print(m3)

What is the problem with this code?

medium

A. The matrices have incompatible dimensions for multiplication

B. The matrix m1 is not square

C. The operator %*% is invalid for matrices

D. The matrix m2 has missing values

Solution

1. Step 1: Check matrix dimensions

   m1 is 2x2, m2 is 3x1 (since 3 values and nrow=3). For multiplication, columns of m1 (2) must equal rows of m2 (3).

2. Step 2: Identify dimension mismatch

   2 != 3, so multiplication is not possible, causing an error.

3. Final Answer:

   The matrices have incompatible dimensions for multiplication -> Option A

4. Quick Check:

   Matrix multiplication needs matching inner dimensions [OK]

Hint: Check if m1 columns = m2 rows before multiplying [OK]

Common Mistakes:

• Assuming any matrices can be multiplied
• Ignoring dimension mismatch errors
• Thinking %*% works element-wise

5. You have two matrices in R:

m1 <- matrix(c(1, 0, 2, -1), nrow=2)
m2 <- matrix(c(3, 1, 4, 2), nrow=2)

You want to compute the matrix product m1 %*% m2 and then subtract the identity matrix of size 2. Which code correctly does this?

hard

A. m3 <- m1 * m2 - diag(2)

B. m3 <- m1 %*% m2 - diag(2)

C. m3 <- m1 %*% m2 - matrix(1, 2, 2)

D. m3 <- m1 %*% m2 - identity(2)

Solution

1. Step 1: Compute matrix multiplication

   Use %*% to multiply m1 and m2 correctly.

2. Step 2: Subtract identity matrix

   Use diag(2) to create a 2x2 identity matrix and subtract it from the product.

3. Final Answer:

   m3 <- m1 %*% m2 - diag(2) -> Option B

4. Quick Check:

   Use diag() for identity matrix in subtraction [OK]

Hint: Use diag(n) for identity matrix, %*% for multiplication [OK]

Common Mistakes:

• Using * instead of %*% for multiplication
• Using matrix(1,2,2) which is all ones, not identity
• Using identity() which is not an R base function