np.linalg.det() for determinant in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the determinant of matrix A.

NumPy

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

Drag options to blanks, or click blank then click option'

Adeterminant_value

Bdeterminant

Cdet

Ddetermin

Attempts:

3 left

💡 Hint

Common Mistakes

Using a wrong function name like 'determinant' or 'determin'.

Trying to call determinant as an attribute instead of a function.

The function to calculate the determinant in numpy is np.linalg.det().

2fill in blank

medium

Complete the code to create a 3x3 matrix and calculate its determinant.

NumPy

import numpy as np
B = np.array([[1, 0, 2], [0, 1, 0], [3, 0, 1]])
det_B = np.linalg.[1](B)
print(det_B)

Drag options to blanks, or click blank then click option'

Adet

Bdeterminant

Cdeterminant_value

Ddetermin

Attempts:

3 left

💡 Hint

Common Mistakes

Using a non-square matrix which causes an error.

Using a wrong function name.

Use np.linalg.det() to calculate the determinant of any square matrix.

3fill in blank

hard

Fix the error in the code to correctly compute the determinant of matrix C.

NumPy

import numpy as np
C = np.array([[2, 5], [1, 3]])
det_C = np.linalg.[1](C)
print(det_C)

Drag options to blanks, or click blank then click option'

Adeterminant

Bdetermin

Cdeterminant_value

Ddet

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'determinant' instead of 'det'.

Misspelling the function name.

The correct function name is det in np.linalg to compute the determinant.

4fill in blank

hard

Fill both blanks to create a 2x2 matrix and calculate its determinant.

NumPy

import numpy as np
matrix = np.array([[[1], [2]], [4, 5]])
det_matrix = np.linalg.det(matrix)
print(det_matrix)

Drag options to blanks, or click blank then click option'

A1

B2

C3

D6

Attempts:

3 left

💡 Hint

Common Mistakes

Using non-numeric values in the matrix.

Creating a non-square matrix.

The matrix is [[1, 2], [4, 5]]. The determinant is calculated using np.linalg.det().

5fill in blank

hard

Fill all three blanks to create a 3x3 matrix and calculate its determinant.

NumPy

import numpy as np
M = np.array([[[1], 0, 0], [0, [2], 0], [0, 0, [3]]])
det_M = np.linalg.det(M)
print(det_M)

Drag options to blanks, or click blank then click option'

A2

B3

C4

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Filling non-diagonal elements with non-zero values.

Using incorrect diagonal values.

The matrix is diagonal with values 5, 3, and 4 on the diagonal. The determinant is the product of these values.

Practice

1. What does the function np.linalg.det() calculate for a square matrix?

easy

A. The inverse of the matrix

B. The determinant of the matrix

C. The transpose of the matrix

D. The sum of all elements in the matrix

Solution

1. Step 1: Understand the purpose of np.linalg.det()

   This function calculates the determinant, a single number that tells if the matrix can be inverted.

2. Step 2: Compare with other matrix operations

   Transpose flips rows and columns, inverse reverses matrix multiplication, sum adds elements. These are different from determinant.

3. Final Answer:

   The determinant of the matrix -> Option B

4. Quick Check:

   np.linalg.det() = determinant [OK]

Hint: Remember: det() means determinant, not inverse or transpose [OK]

Common Mistakes:

• Confusing determinant with inverse
• Thinking it returns a matrix instead of a number
• Mixing up with transpose operation

2. Which of the following is the correct syntax to calculate the determinant of a matrix mat using numpy?

easy

A. np.linalg.determinant(mat)

B. np.det.linalg(mat)

C. np.linalg.det(mat)

D. np.det(mat)

Solution

1. Step 1: Recall the correct numpy function

   The determinant function is inside the linalg module and is called det().

2. Step 2: Check the syntax

   The correct call is np.linalg.det(mat). Other options have wrong order or function names.

3. Final Answer:

   np.linalg.det(mat) -> Option C

4. Quick Check:

   Correct syntax = np.linalg.det(mat) [OK]

Hint: Use np.linalg.det() exactly, no shortcuts [OK]

Common Mistakes:

• Swapping 'det' and 'linalg' order
• Using non-existent function names
• Omitting the linalg module

3. What is the output of the following code?

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

medium

A. 2.0

B. 10.0

C. 11.0

D. 5.0

Solution

1. Step 1: Calculate determinant manually

   For matrix [[2,3],[1,4]], determinant = (2*4) - (3*1) = 8 - 3 = 5.

2. Step 2: Confirm output with rounding

   Rounding 5 to 2 decimals remains 5.0, matching printed output.

3. Final Answer:

   5.0 -> Option D

4. Quick Check:

   Determinant = 5.0 [OK]

Hint: Determinant 2x2 = ad - bc, calculate quickly [OK]

Common Mistakes:

• Multiplying all elements instead of ad - bc
• Forgetting to subtract
• Rounding errors without rounding function

4. The code below throws an error. What is the main reason?

import numpy as np
mat = np.array([[1, 2, 3], [4, 5, 6]])
print(np.linalg.det(mat))

medium

A. Matrix is not square

B. np.linalg.det() does not exist

C. Matrix contains integers instead of floats

D. Missing import statement

Solution

1. Step 1: Check matrix shape

   The matrix shape is (2,3), which is not square (rows != columns).

2. Step 2: Understand determinant requirements

   Determinant is defined only for square matrices, so np.linalg.det() raises an error.

3. Final Answer:

   Matrix is not square -> Option A

4. Quick Check:

   Non-square matrix causes error [OK]

Hint: Determinant needs square matrix, check shape first [OK]

Common Mistakes:

• Assuming det works on any matrix shape
• Thinking data type causes error
• Ignoring error message about shape

5. You have a 3x3 matrix:

mat = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

What does a determinant of zero imply about this matrix?

hard

A. The matrix is singular and has no inverse

B. The matrix is invertible

C. The matrix is diagonal

D. The matrix is symmetric

Solution

1. Step 1: Understand determinant zero meaning

   A zero determinant means the matrix is singular, so it cannot be inverted.

2. Step 2: Check matrix properties

   Matrix is not invertible, but zero determinant does not imply diagonal or symmetric properties.

3. Final Answer:

   The matrix is singular and has no inverse -> Option A

4. Quick Check:

   Determinant zero = no inverse [OK]

Hint: Zero determinant means no inverse exists [OK]

Common Mistakes:

• Thinking zero determinant means invertible
• Confusing diagonal or symmetric with determinant
• Ignoring singular matrix definition