Matrix determinant (det) in SciPy - 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 how it scales space.

beginner

How do you calculate the determinant of a matrix using scipy?

Use scipy.linalg.det(matrix) where matrix is a square numpy array.

beginner

What does a determinant value of zero mean for a matrix?

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

intermediate

If a matrix has a determinant of 5, what does that tell us about the matrix?

The matrix is invertible and it scales volumes by a factor of 5.

beginner

Write a simple Python code snippet using scipy to find the determinant of a 2x2 matrix [[1, 2], [3, 4]].

import numpy as np
from scipy.linalg import det
matrix = np.array([[1, 2], [3, 4]])
determinant = det(matrix)
print(determinant)

Which function from scipy calculates the determinant of a matrix?

A scipy.linalg.inv

B scipy.linalg.det

C scipy.linalg.eig

D scipy.linalg.norm

The function scipy.linalg.det computes the determinant of a square matrix.

What does a zero determinant indicate about a matrix?

A Matrix is symmetric

B Matrix is invertible

C Matrix is diagonal

D Matrix is singular

A zero determinant means the matrix is singular and does not have an inverse.

If the determinant of a matrix is negative, what does it imply?

A Matrix scales space and flips orientation

B Matrix is not square

C Matrix is singular

D Matrix is identity

A negative determinant means the matrix flips the orientation of space while scaling.

Which of these matrices can have a determinant calculated?

A Only square matrices

B Any rectangular matrix

C Only diagonal matrices

D Only symmetric matrices

Determinants are defined only for square matrices.

What is the determinant of the identity matrix?

A 0

B -1

C 1

D Depends on size

The determinant of the identity matrix is always 1, regardless of its size.

Explain what the determinant of a matrix tells us about the matrix's properties.

Think about how the matrix changes space and if it can be reversed.

Describe how to compute the determinant of a matrix using scipy and interpret the result.

Focus on the function name and what the output number means.