Matrix determinant (det) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate determinant of a 2x2 matrix

What is the output of this code that calculates the determinant of a 2x2 matrix using scipy?

SciPy

import numpy as np
from scipy.linalg import det
matrix = np.array([[4, 7], [2, 6]])
result = det(matrix)
print(round(result, 2))

A 14.0

B 10.0

C 0.0

D 26.0

💡 Hint

Recall determinant formula for 2x2: ad - bc

The determinant of [[4,7],[2,6]] is (4*6) - (7*2) = 24 - 14 = 10.

❓ data_output

intermediate

Number of matrices with zero determinant

Given these three matrices, how many have a determinant of zero?

SciPy

import numpy as np
from scipy.linalg import det
matrices = [
  np.array([[1, 2], [2, 4]]),
  np.array([[3, 0], [0, 3]]),
  np.array([[0, 1], [1, 0]])
]
zero_det_count = sum(abs(det(m)) < 1e-10 for m in matrices)
print(zero_det_count)

A 1

B 0

C 3

D 2

💡 Hint

Check if rows are linearly dependent for zero determinant.

Only the first matrix has determinant zero because its rows are multiples (2*row1 = row2).

🔧 Debug

advanced

Identify the error in determinant calculation

What error does this code raise when trying to calculate the determinant?

SciPy

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

A ValueError: expected square matrix

B TypeError: det() argument must be a matrix

C AttributeError: 'numpy.ndarray' object has no attribute 'det'

D No error, outputs 0

💡 Hint

Check the shape of the input array.

The input is a 1D array, not a 2D square matrix, so scipy.linalg.det raises ValueError.

🧠 Conceptual

advanced

Effect of row swap on determinant

If you swap two rows of a square matrix, how does the determinant change?

A It becomes zero

B It doubles

C It changes sign (multiplied by -1)

D It remains the same

💡 Hint

Think about how row operations affect determinants.

Swapping two rows multiplies the determinant by -1, changing its sign.

🚀 Application

expert

Determinant of product of matrices

Given two square matrices A and B, what is the determinant of their product AB?

A det(AB) = det(A) + det(B)

B det(AB) = det(A) / det(B)

C det(AB) = det(A) - det(B)

D det(AB) = det(A) * det(B)

💡 Hint

Recall properties of determinants with matrix multiplication.

The determinant of a product is the product of determinants: det(AB) = det(A) * det(B).