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.

Practice

1.

What does the MATLAB function det(A) compute when A is a square matrix?

easy

A. The determinant of matrix A

B. The transpose of matrix A

C. The inverse of matrix A

D. The sum of all elements in matrix A

Solution

1. Step 1: Understand the function purpose

   The function det(A) in MATLAB calculates a single number called the determinant for a square matrix A.

2. Step 2: Recall determinant meaning

   The determinant tells us about matrix properties like invertibility, not transpose, inverse, or sum.

3. Final Answer:

   The determinant of matrix A -> Option A

4. Quick Check:

   det(A) = determinant [OK]

Hint: Remember det() always returns a single number for square matrices [OK]

Common Mistakes:

• Confusing determinant with transpose
• Thinking det() returns a matrix
• Mixing determinant with sum of elements

2.

Which of the following is the correct MATLAB syntax to find the determinant of matrix M?

?

easy

A. determinant(M)

B. det(M)

C. determinant = M

D. determinant(M);

Solution

1. Step 1: Identify MATLAB function for determinant

   The correct MATLAB function to compute determinant is det().

2. Step 2: Check syntax correctness

   The correct syntax is det(M). Other options use wrong function names or incorrect assignment.

3. Final Answer:

   det(M) -> Option B

4. Quick Check:

   Use det(M) to get determinant [OK]

Hint: Use det() exactly, no extra words or assignments [OK]

Common Mistakes:

• Using 'determinant' instead of 'det'
• Adding semicolon inside function call
• Assigning determinant without function

3.

What is the output of the following MATLAB code?

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

medium

A. -5

B. 11

C. 10

D. 5

Solution

1. Step 1: Calculate determinant of matrix A

   Matrix A = [2 3; 1 4]. Determinant = (2*4) - (3*1) = 8 - 3 = 5.

2. Step 2: Assign and display determinant

   Variable d stores 5, so output is 5.

3. Final Answer:

   5 -> Option D

4. Quick Check:

   det([2 3;1 4]) = 5 [OK]

Hint: Use formula ad-bc for 2x2 matrix determinant [OK]

Common Mistakes:

• Multiplying elements incorrectly
• Swapping terms in subtraction
• Confusing determinant with sum

4.

Identify the error in this MATLAB code snippet:

B = [1 2 3; 4 5 6];
detB = det(B);

medium

A. Variable detB is not defined properly

B. Syntax error in det function call

C. Matrix B is not square, so det(B) causes an error

D. No error, code runs fine

Solution

1. Step 1: Check matrix dimensions

   Matrix B is 2x3, which is not square.

2. Step 2: Understand det() requirements

   det() requires a square matrix; using it on non-square matrix causes an error.

3. Final Answer:

   Matrix B is not square, so det(B) causes an error -> Option C

4. Quick Check:

   det() needs square matrix [OK]

Hint: Only square matrices have determinants [OK]

Common Mistakes:

• Trying det() on non-square matrix
• Ignoring matrix size requirements
• Assuming det() returns zero for non-square

5.

Given matrix C = [1 2 3; 0 1 4; 5 6 0], which MATLAB code correctly checks if C is invertible using its determinant?

hard

A. if det(C) ~= 0
disp('Invertible')
else
disp('Not invertible')
end

B. if det(C) == 0
disp('Invertible')
else
disp('Not invertible')
end

C. if det(C) > 1
disp('Invertible')
else
disp('Not invertible')
end

D. if det(C) < 0
disp('Invertible')
else
disp('Not invertible')
end

Solution

1. Step 1: Recall invertibility condition

   A matrix is invertible if its determinant is not zero.

2. Step 2: Analyze code options

   if det(C) ~= 0 disp('Invertible') else disp('Not invertible') end checks if det(C) ~= 0, correctly identifying invertibility. Others check wrong conditions.

3. Final Answer:

   if det(C) ~= 0 disp('Invertible') else disp('Not invertible') end -> Option A

4. Quick Check:

   Invertible if det ≠ 0 [OK]

Hint: Invertible means determinant not zero [OK]

Common Mistakes:

• Checking det == 0 for invertibility
• Using > 1 or < 0 instead of zero check
• Confusing invertible with positive determinant