Matrix determinant (det) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this MATLAB code?

Consider the following MATLAB code that calculates the determinant of a matrix. What is the output printed to the console?

MATLAB

A = [2 3; 1 4];
d = det(A);
disp(d);

A 10

B 11

C 14

D 5

💡 Hint

Recall that the determinant of a 2x2 matrix [a b; c d] is ad - bc.

The determinant of matrix A = [2 3; 1 4] is (2*4) - (3*1) = 8 - 3 = 5.

❓ Predict Output

intermediate

What is the determinant of this 3x3 matrix?

Given the matrix B below, what value does MATLAB's det(B) return?

MATLAB

B = [1 2 3; 0 1 4; 5 6 0];
d = det(B);
disp(d);

A 24

B 1

C 0

D -1

💡 Hint

Use the rule for 3x3 determinants or MATLAB's det function.

The determinant is calculated as 1*(1*0 - 4*6) - 2*(0*0 - 4*5) + 3*(0*6 - 1*5) = 1*(0 - 24) - 2*(0 - 20) + 3*(0 - 5) = -24 + 40 - 15 = 1.

❓ Predict Output

advanced

What is the output of this MATLAB code with a singular matrix?

What does MATLAB display when calculating the determinant of matrix C?

MATLAB

C = [1 2 3; 2 4 6; 3 6 9];
d = det(C);
disp(d);

A 12

B 1

C 0

D NaN

💡 Hint

Check if the rows of the matrix are linearly dependent.

Matrix C has rows that are multiples of each other, so it is singular and its determinant is 0.

❓ Predict Output

advanced

What is the determinant of this diagonal matrix?

Calculate the determinant of matrix D using MATLAB's det function. What is the output?

MATLAB

D = diag([4, 5, 6, 7]);
d = det(D);
disp(d);

A 840

B 22

C 0

D 1

💡 Hint

The determinant of a diagonal matrix is the product of its diagonal elements.

The determinant is 4*5*6*7 = 840.

🧠 Conceptual

expert

What error does this MATLAB code produce?

What error message will MATLAB show when running this code?

MATLAB

E = [1 2; 3 4; 5 6];
d = det(E);
disp(d);

A Error using det: Input must be a square matrix.

B 0

C NaN

D 6

💡 Hint

Check the shape of matrix E and the requirements for det.

The det function requires a square matrix. E is 3x2, so MATLAB throws an error.