np.linalg.det() for determinant in NumPy - 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 np.linalg.det()?

NumPy

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

A 0.0

B 26.0

C 1.0

D 10.0

💡 Hint

Recall the formula for determinant of 2x2 matrix [[a, b], [c, d]] is ad - bc.

The determinant is calculated as (4*6) - (7*2) = 24 - 14 = 10.0.

❓ data_output

intermediate

Determinant of a singular matrix

What is the value of det after running this code for a singular matrix?

NumPy

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

A 0.0

B 2.0

C 1.0

D -2.0

💡 Hint

A singular matrix has determinant zero.

The second row is twice the first, so determinant is zero.

🔧 Debug

advanced

Identify the error in determinant calculation

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

NumPy

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

A ValueError: could not broadcast input array from shape (4,) into shape (2,2)

B TypeError: unsupported operand type(s) for -: 'int' and 'str'

C LinAlgError: Last 2 dimensions of the array must be square

D No error, prints 0.0

💡 Hint

Check the shape of the input array for determinant calculation.

The input is a 1D array, but determinant requires a 2D square matrix.

🚀 Application

advanced

Using determinant to check matrix invertibility

Which option correctly checks if a matrix is invertible using its determinant?

NumPy

import numpy as np
matrix = np.array([[3, 1], [2, 4]])
det = np.linalg.det(matrix)
# Check invertibility here

A

if det > 0:
    print('Invertible')
else:
    print('Not invertible')

B

if det != 0:
    print('Invertible')
else:
    print('Not invertible')

C

if det == 1:
    print('Invertible')
else:
    print('Not invertible')

D

if det < 0:
    print('Invertible')
else:
    print('Not invertible')

💡 Hint

A matrix is invertible if its determinant is not zero.

Only non-zero determinant means matrix is invertible regardless of sign.

🧠 Conceptual

expert

Effect of row operations on determinant

If you multiply one row of a square matrix by 3, how does the determinant change?

A The determinant is multiplied by 3

B The determinant remains the same

C The determinant is multiplied by 9

D The determinant becomes zero

💡 Hint

Think about how scaling a row affects volume represented by determinant.

Multiplying one row by a scalar multiplies determinant by that scalar.