Matrix determinant (det) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the determinant of a matrix?

The determinant is a single number that summarizes some properties of a square matrix, like whether it is invertible or not.

beginner

How do you calculate the determinant of a matrix in MATLAB?

Use the function det(A), where A is your square matrix.

intermediate

What does it mean if the determinant of a matrix is zero?

It means the matrix is singular and does not have an inverse. It also means the matrix squashes space into a lower dimension.

beginner

What is the determinant of a 2x2 matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \)?

The determinant is calculated as \( ad - bc \).

intermediate

Why is the determinant useful in real life?

It helps us understand if systems of equations have solutions, if transformations flip or shrink shapes, and in physics for volume scaling.

Which MATLAB function calculates the determinant of a matrix?

A eig()

B inv()

C rank()

D det()

The det() function returns the determinant of a square matrix.

What does a zero determinant indicate about a matrix?

A Matrix is singular

B Matrix is identity

C Matrix is diagonal

D Matrix is invertible

A zero determinant means the matrix is singular and cannot be inverted.

What is the determinant of the matrix \( \begin{bmatrix} 3 & 4 \\ 2 & 1 \end{bmatrix} \)?

A -5

B 10

C 5

D -10

Determinant = (3*1) - (4*2) = 3 - 8 = -5.

Which of these is NOT true about determinants?

A Determinant can be used to check if a matrix is invertible

B Determinant is always positive

C Determinant is a single number

D Determinant changes sign if two rows are swapped

Determinants can be positive, negative, or zero.

In MATLAB, what happens if you try to find the determinant of a non-square matrix?

A Returns 0

B Returns 1

C Throws an error

D Calculates determinant anyway

The determinant is only defined for square matrices, so MATLAB throws an error.

Explain how to calculate the determinant of a 2x2 matrix and what the result tells you about the matrix.

Think about the simple 2x2 matrix and what the determinant number means.

Describe how the MATLAB function det() is used and what kind of input it requires.

Remember the function name and input shape.