Matrix determinant (det) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the determinant of matrix A.

MATLAB

d = [1](A);

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

Adet

Bsum

Cprod

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum or prod instead of det.

Trying to invert the matrix instead of finding determinant.

The det function calculates the determinant of a matrix in MATLAB.

2fill in blank

medium

Complete the code to calculate the determinant of a 2x2 matrix M.

MATLAB

d = [1](M);

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

Ainv

Brank

Cdet

Dtrace

Attempts:

3 left

💡 Hint

Common Mistakes

Using inv or rank instead of det.

Using trace which sums diagonal elements.

The det function computes the determinant of matrix M.

3fill in blank

hard

Fix the error in the code to correctly compute the determinant of matrix B.

MATLAB

determinant = [1](B);

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

Adet

Bsum

Cprod

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum or prod instead of det.

Using inv which computes inverse.

The correct function to compute determinant is det.

4fill in blank

hard

Fill both blanks to create a function that returns the determinant of input matrix X.

MATLAB

function d = [1](X)
    d = [2](X);
end

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

AmyDet

Bdet

Csum

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum or inv inside the function instead of det.

Not defining a function name.

The function name can be myDet, and inside it calls det to compute the determinant.

5fill in blank

hard

Fill all three blanks to compute and display the determinant of matrix A.

MATLAB

A = [1 2; 3 4];
d = [1](A);
disp([[2] num2str([3])]);

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

Adet

B'Determinant is: '

Cd

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum instead of det.

Not converting number to string before concatenation.

Using wrong variable names.

Use det to get determinant, then display the message with disp combining text and the value.

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