Transpose and inverse in R Programming - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to transpose matrix m.

R Programming

t_m <- [1](m)

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

Atranspose

Bt

Cinv

Dsolve

Attempts:

3 left

💡 Hint

Common Mistakes

Using solve() instead of t() for transpose

Using inv() which is not a base R function

The t() function transposes a matrix in R.

2fill in blank

medium

Complete the code to find the inverse of matrix m.

R Programming

inv_m <- [1](m)

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

Asolve

Binverse

Ct

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using t() which transposes, not inverts

Using inv() which is not a base R function

The solve() function computes the inverse of a matrix in R.

3fill in blank

hard

Fix the error in the code to correctly compute the inverse of matrix m.

R Programming

inverse_m <- [1](m)

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

Atranspose

Binv

Ct

Dsolve

Attempts:

3 left

💡 Hint

Common Mistakes

Using inv() which is not defined

Using t() which transposes instead of inverts

Only solve() correctly computes the inverse in base R.

4fill in blank

hard

Fill both blanks to create a matrix m and then transpose it.

R Programming

m <- matrix(c(1, 2, 3, 4), nrow = [1], ncol = [2])
t_m <- t(m)

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

A2

B3

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting nrow or ncol incorrectly causing dimension mismatch

The matrix has 2 rows and 2 columns as per the data vector length.

5fill in blank

hard

Fill all three blanks to create a matrix, find its inverse, and then transpose the inverse.

R Programming

m <- matrix(c(4, 7, 2, 6), nrow = [1], ncol = [2])
inv_m <- [3](m)
t_inv_m <- t(inv_m)

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

A2

Csolve

Dt

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong dimensions for the matrix

Using t() instead of solve() for inversion

The matrix is 2x2, solve() finds its inverse, then t() transposes it.

Practice

1.

What does the t() function do when applied to a matrix in R?

easy

A. It sums all elements of the matrix.

B. It calculates the inverse of the matrix.

C. It multiplies the matrix by itself.

D. It flips the matrix over its diagonal (transpose).

Solution

1. Step 1: Understand the function t()

   The t() function in R is used to transpose a matrix, which means flipping it over its diagonal.

2. Step 2: Identify the effect on the matrix

   Transposing swaps rows and columns, so the element at row i, column j moves to row j, column i.

3. Final Answer:

   It flips the matrix over its diagonal (transpose). -> Option D

4. Quick Check:

   t() = transpose [OK]

Hint: Transpose flips rows and columns across the diagonal [OK]

Common Mistakes:

• Confusing transpose with inverse
• Thinking it sums matrix elements
• Assuming it multiplies matrix by itself

2.

Which of the following is the correct syntax to find the inverse of a square matrix A in R?

easy

A. inv(A)

B. inverse(A)

C. solve(A)

D. t(A)

Solution

1. Step 1: Recall the function for matrix inverse in R

   In R, the function solve() is used to compute the inverse of a square matrix.

2. Step 2: Check the options

   Only solve(A) correctly computes the inverse. t(A) transposes, others are invalid.

3. Final Answer:

   solve(A) -> Option C

4. Quick Check:

   solve() = inverse [OK]

Hint: Use solve() to invert matrices in R [OK]

Common Mistakes:

• Using t() instead of solve() for inverse
• Assuming inverse() or inv() exist in base R
• Confusing transpose with inverse

3.

What is the output of the following R code?

A <- matrix(c(1, 2, 3, 4), nrow=2, byrow=TRUE)
B <- t(A)
B

medium

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

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

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

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

Solution

1. Step 1: Create matrix A

   Matrix A is 2x2 with rows: [1, 2] and [3, 4].

2. Step 2: Transpose matrix A to get B

   Transposing swaps rows and columns, so B's first row is [1, 3], second row is [2, 4].

3. Final Answer:

   [1, 3] [2, 4] -> Option A

4. Quick Check:

   Transpose swaps rows and columns [OK]

Hint: Transpose swaps rows and columns [OK]

Common Mistakes:

• Confusing original matrix with transpose
• Mixing row-wise and column-wise order
• Reading matrix elements incorrectly

4.

Consider the code below. What is the error and how to fix it?

A <- matrix(c(1, 2, 3, 4, 5, 6), nrow=2)
invA <- solve(A)
invA

medium

A. No error; code runs fine and returns inverse.

B. Error: matrix is not square; fix by making it square (e.g., 2x2).

C. Error: solve() requires a vector; fix by passing a vector.

D. Error: matrix contains non-numeric values; fix data type.

Solution

1. Step 1: Check matrix dimensions

   Matrix A has 2 rows and 3 columns, so it is not square.

2. Step 2: Understand solve() requirements

   The solve() function requires a square matrix to compute its inverse.

3. Step 3: Fix the error

   Make A square by changing number of elements or rows/columns, e.g., 2x2 matrix.

4. Final Answer:

   Error: matrix is not square; fix by making it square (e.g., 2x2). -> Option B

5. Quick Check:

   Inverse needs square matrix [OK]

Hint: Inverse requires square matrix; check dimensions first [OK]

Common Mistakes:

• Trying to invert non-square matrix
• Ignoring error messages from solve()
• Assuming solve() works on any matrix shape

5.

You have a 3x3 matrix M. You want to check if multiplying M by its inverse returns the identity matrix. Which R code correctly performs this check?

hard

A. identity_check <- M %*% solve(M); all(identity_check == diag(3))

B. identity_check <- t(M) %*% solve(M); all(identity_check == diag(3))

C. identity_check <- solve(M) %*% M; all(identity_check == matrix(1,3,3))

D. identity_check <- M %*% M; all(identity_check == diag(3))

Solution

1. Step 1: Multiply matrix by its inverse

   Multiplying M by solve(M) should give the identity matrix.

2. Step 2: Check equality with identity matrix

   Use diag(3) to create 3x3 identity matrix and compare with result using all().

3. Step 3: Analyze options

   identity_check <- M %*% solve(M); all(identity_check == diag(3)) correctly multiplies M %*% solve(M) and compares to identity. identity_check <- t(M) %*% solve(M); all(identity_check == diag(3)) uses transpose incorrectly. identity_check <- solve(M) %*% M; all(identity_check == matrix(1,3,3)) compares to a matrix of ones, which is wrong. identity_check <- M %*% M; all(identity_check == diag(3)) multiplies M by itself, not inverse.

4. Final Answer:

   identity_check <- M %*% solve(M); all(identity_check == diag(3)) -> Option A

5. Quick Check:

   Matrix times inverse = identity [OK]

Hint: Multiply matrix by solve(matrix) to get identity [OK]

Common Mistakes:

• Using transpose instead of inverse
• Comparing to matrix of ones instead of identity
• Multiplying matrix by itself instead of inverse