Matrix inverse (inv) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the inverse of matrix A.

MATLAB

B = [1](A);

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

Ainv

Binverse

Cinvert

Dinver

Attempts:

3 left

💡 Hint

Common Mistakes

Using a non-existent function like 'inverse' or 'invert'.

Misspelling the function name.

The inv function in MATLAB calculates the inverse of a matrix.

2fill in blank

medium

Complete the code to compute the inverse of a 3x3 matrix M.

MATLAB

invM = [1](M);

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

Ainvert

Binv

Cinver

Dinverse

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect function names.

Trying to use functions that do not exist in MATLAB.

Use inv to find the inverse of matrix M.

3fill in blank

hard

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

MATLAB

Y = [1](X);

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

Ainvers

Binvert

Cinver

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using misspelled function names.

Using non-existent functions.

The correct MATLAB function to compute the inverse is inv.

4fill in blank

hard

Fill both blanks to create a matrix inverse and multiply it by the original matrix.

MATLAB

invA = [1](A);
I = A [2] invA;

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

Ainv

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication.

Using incorrect function names.

Use inv to get the inverse, then multiply A by its inverse using *.

5fill in blank

hard

Fill all three blanks to compute the inverse of matrix B, multiply it by vector v, and store the result in x.

MATLAB

invB = [1](B);
x = invB [2] v;
result = [3];

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

Ainv

B*

Cx

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication.

Using wrong variable names.

Misspelling the inverse function.

First, compute the inverse with inv, then multiply by v using *, and finally assign the product to result.

Practice

1.

What does the MATLAB function inv(A) do when A is a square matrix?

easy

A. Calculates the eigenvalues of matrix A

B. Calculates the transpose of matrix A

C. Calculates the inverse of matrix A

D. Calculates the determinant of matrix A

Solution

1. Step 1: Understand the function purpose

   The function inv in MATLAB is designed to compute the inverse of a square matrix.

2. Step 2: Recall matrix inverse definition

   The inverse of a matrix A is a matrix B such that A * B = I, where I is the identity matrix.

3. Final Answer:

   Calculates the inverse of matrix A -> Option C

4. Quick Check:

   inv(A) = inverse of A [OK]

Hint: inv() finds matrix inverse, not transpose or determinant [OK]

Common Mistakes:

• Confusing inverse with transpose
• Thinking inv() calculates determinant
• Assuming inv() returns eigenvalues

2.

Which of the following is the correct syntax to compute the inverse of a matrix A in MATLAB?

easy

A. A\inv

B. inverse(A)

C. A.inv()

D. inv(A)

Solution

1. Step 1: Recall MATLAB function for inverse

   MATLAB uses the function inv() to compute the inverse of a matrix.

2. Step 2: Check syntax correctness

   The correct syntax is inv(A). Other options are not valid MATLAB syntax for matrix inverse.

3. Final Answer:

   inv(A) -> Option D

4. Quick Check:

   Use inv(A) to invert matrix A [OK]

Hint: Use inv(A) function, not inverse() or dot notation [OK]

Common Mistakes:

• Using inverse(A) instead of inv(A)
• Trying object-oriented syntax like A.inv()
• Confusing backslash operator with inv()

3.

What is the output of the following MATLAB code?

A = [1 2; 3 4]; B = inv(A); disp(round(B,2));

medium

A. [[-2.00 1.00]; [1.50 -0.50]]

B. [[4.00 -2.00]; [-3.00 1.00]]

C. [[1.00 3.00]; [2.00 4.00]]

D. Error: Matrix is singular

Solution

1. Step 1: Calculate determinant of A

   det(A) = (1*4) - (2*3) = 4 - 6 = -2 (non-zero, so inverse exists)

2. Step 2: Compute inverse of A

   Inverse formula for 2x2 matrix: (1/det) * [d -b; -c a] = (1/-2) * [4 -2; -3 1] = [[-2 1]; [1.5 -0.5]]

3. Final Answer:

   [[-2.00 1.00]; [1.50 -0.50]] -> Option A

4. Quick Check:

   inv(A) = [[-2 1]; [1.5 -0.5]] [OK]

Hint: Use formula for 2x2 inverse: swap diagonal, negate off-diagonal [OK]

Common Mistakes:

• Mixing up signs in inverse formula
• Calculating determinant incorrectly
• Confusing inverse with transpose

4.

Consider this MATLAB code snippet:

A = [1 2; 2 4]; B = inv(A); disp(B);

What is the problem with this code?

medium

A. Matrix A is not square

B. Matrix A is singular and cannot be inverted

C. Syntax error in inv function usage

D. Matrix A is not numeric

Solution

1. Step 1: Check matrix shape

   Matrix A is 2x2, so it is square, no problem here.

2. Step 2: Check if matrix is invertible

   Calculate determinant: det(A) = (1*4) - (2*2) = 4 - 4 = 0, so A is singular and cannot be inverted.

3. Final Answer:

   Matrix A is singular and cannot be inverted -> Option B

4. Quick Check:

   det(A) = 0 means no inverse [OK]

Hint: Check determinant; zero means no inverse [OK]

Common Mistakes:

• Assuming all square matrices are invertible
• Ignoring determinant calculation
• Thinking syntax error causes failure

5.

You have a system of linear equations represented by A * x = b, where A is a 3x3 matrix and b is a vector. Which MATLAB command is the best practice to find x?

hard

A. x = A \ b;

B. x = inv(A) * b;

C. x = A / b;

D. x = b * inv(A);

Solution

1. Step 1: Understand solving linear systems in MATLAB

   Using inv(A)*b works but is inefficient and less accurate.

2. Step 2: Use MATLAB backslash operator

   The recommended way is x = A \ b; which solves the system efficiently without explicitly computing inverse.

3. Final Answer:

   x = A \ b; -> Option A

4. Quick Check:

   Use backslash \ for solving Ax=b, not inv(A) [OK]

Hint: Use backslash \ operator to solve linear systems [OK]

Common Mistakes:

• Using inv(A)*b which is slower and less stable
• Using division operators incorrectly
• Multiplying b by inv(A) instead of inv(A)*b