Matrix determinant (det) in MATLAB - Mini Project: Build & Apply

Matrix determinant (det)

📖 Scenario: You are working with square matrices in MATLAB. You want to find the determinant of a matrix, which is a special number that tells you important things about the matrix, like if it can be inverted.

🎯 Goal: Build a MATLAB script that creates a matrix, sets a size threshold, calculates the determinant only if the matrix size is within the threshold, and then displays the determinant.

📋 What You'll Learn

Create a 3x3 matrix called A with exact values: [1 2 3; 4 5 6; 7 8 9]

Create a variable called max_size and set it to 3

Calculate the determinant of A only if the number of rows in A is less than or equal to max_size, store it in det_A

Display the value of det_A using disp

💡 Why This Matters

🌍 Real World

Calculating determinants helps in solving systems of equations, checking matrix invertibility, and understanding matrix properties in engineering and science.

💼 Career

Matrix operations like determinant calculation are fundamental in data analysis, computer graphics, machine learning, and scientific computing jobs.

1

Create the matrix A

Create a 3x3 matrix called A with these exact values: [1 2 3; 4 5 6; 7 8 9]

MATLAB

% Create matrix A with the given values
% Your code here

Hint

Use square brackets and semicolons to create rows in MATLAB.

2

Set the size threshold max_size

Create a variable called max_size and set it to 3

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
% Set max_size to 3
% Your code here

Hint

Just assign the number 3 to the variable max_size.

3

Calculate the determinant if size condition is met

Calculate the determinant of A only if the number of rows in A is less than or equal to max_size. Store the result in det_A. Use size(A,1) to get the number of rows and det(A) to calculate the determinant.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
max_size = 3;
% Calculate determinant if size condition is met
% Your code here

Hint

Use an if statement to check the size, then calculate determinant with det(A).

4

Display the determinant det_A

Use disp(det_A) to display the value of the determinant stored in det_A.

MATLAB

A = [1 2 3; 4 5 6; 7 8 9];
max_size = 3;
if size(A,1) <= max_size
    det_A = det(A);
else
    det_A = NaN; % Not calculated if size too big
end
% Display the determinant
% Your code here

Hint

Use disp(det_A) to show the determinant on the screen.

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