Matrix inverse (inv) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of matrix inverse multiplication

What is the output of this MATLAB code snippet?

MATLAB

A = [2 1; 5 3];
B = inv(A) * A;

A [1 0; 0 1]

B [0 1; 1 0]

C [2 1; 5 3]

D Error: Matrix is singular

💡 Hint

Multiplying a matrix by its inverse results in the identity matrix.

The inverse of matrix A multiplied by A returns the identity matrix of the same size.

❓ Predict Output

intermediate

Result of inverse on singular matrix

What happens when you run this MATLAB code?

MATLAB

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

A [1 2; 2 4]

B Error: Matrix is singular to working precision.

C [0.5 -0.25; -0.25 0.125]

D Error: Matrix must be square.

💡 Hint

Check if the matrix has linearly dependent rows.

Matrix A is singular because its rows are linearly dependent, so inv(A) throws an error.

🔧 Debug

advanced

Identify the error in matrix inverse calculation

What error does this MATLAB code produce?

MATLAB

A = [1 2 3; 4 5 6];
B = inv(A);

A Error: Matrix must be square.

B [0.5 -0.5 0; -0.5 0.5 0]

C [1 0 0; 0 1 0; 0 0 1]

D Error: Matrix is singular.

💡 Hint

Check the shape of the matrix before inversion.

The inv function requires a square matrix; A is 2x3, so MATLAB throws an error.

❓ Predict Output

advanced

Inverse of a diagonal matrix

What is the output of this MATLAB code?

MATLAB

D = diag([4 5 6]);
E = inv(D);

A Error: Matrix is singular.

B [4 5 6; 0 0 0; 0 0 0]

C [1 0 0; 0 1 0; 0 0 1]

D [0.25 0 0; 0 0.2 0; 0 0 0.1667]

💡 Hint

The inverse of a diagonal matrix is a diagonal matrix with reciprocal elements.

The inverse of a diagonal matrix has diagonal elements that are the reciprocals of the original.

🧠 Conceptual

expert

Properties of matrix inverse and multiplication

Given a nonsingular matrix A, which statement is TRUE?

A inv(A + B) = inv(A) + inv(B)

B inv(A * B) = inv(A) * inv(B)

C inv(A * B) = inv(B) * inv(A)

D inv(A) * A = zeros(size(A))

💡 Hint

Recall the order of multiplication when inverting a product.

The inverse of a product is the product of the inverses in reverse order: inv(A*B) = inv(B)*inv(A).