Matrix determinant (det) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function that calculates the determinant of a matrix.

SciPy

from scipy.linalg import [1]

matrix = [[1, 2], [3, 4]]
result = det(matrix)
print(result)

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

Adet

Bdeterminant

Cdetermin

Ddeterminant_calc

Attempts:

3 left

💡 Hint

Common Mistakes

Using a wrong function name like 'determinant' which does not exist in scipy.linalg.

Trying to import from numpy.linalg instead of scipy.linalg.

The function to calculate the determinant in scipy.linalg is det.

2fill in blank

medium

Complete the code to calculate the determinant of the given matrix.

SciPy

from scipy.linalg import det

matrix = [[2, 3], [1, 4]]
determinant = [1](matrix)
print(determinant)

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

Adet_calc

Bdet

Cdetermin

Ddeterminant

Attempts:

3 left

💡 Hint

Common Mistakes

Calling a function that is not imported or does not exist.

Trying to call 'determinant' which is not defined.

The function to calculate the determinant is det. Use it by passing the matrix.

3fill in blank

hard

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

SciPy

from scipy.linalg import det

matrix = [[1, 2, 3], [4, 5, 6]]
det_value = [1](matrix)
print(det_value)

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

Adetermin

Bdeterminant

Cdet_calc

Ddet

Attempts:

3 left

💡 Hint

Common Mistakes

Using a wrong function name.

Trying to calculate determinant of a non-square matrix (which causes runtime error).

The matrix must be square to compute determinant. The function is det. However, the matrix here is not square, so the code will error at runtime. But the question asks to fix the function call, so det is correct.

4fill in blank

hard

Fill both blanks to create a dictionary of determinants for matrices with size 2 and 3.

SciPy

from scipy.linalg import det

matrices = {
    2: [[1, 2], [3, 4]],
    3: [[1, 0, 2], [0, 1, 5], [3, 2, 1]]
}
determinants = {size: det([1]) for size, [2] in matrices.items()}
print(determinants)

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

Amatrix

Bmat

Cmatrixes

Dm

Attempts:

3 left

💡 Hint

Common Mistakes

Using the key instead of the value for determinant calculation.

Using variable names not matching the iteration unpacking.

In the dictionary comprehension, the value for each key is the matrix, so both blanks are filled with the same variable name for the matrix value, commonly mat.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that stores determinants of matrices with keys as uppercase size names.

SciPy

from scipy.linalg import det

matrices = {
    'two': [[2, 0], [0, 2]],
    'three': [[1, 2, 3], [0, 1, 4], [5, 6, 0]]
}
determinants = [1]([2].upper(): [3](matrix) for [2], matrix in matrices.items())
print(determinants)

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

Adict

Bkey

Cdet

Dvalue

Attempts:

3 left

💡 Hint

Common Mistakes

Using the same variable name for both key and value in the comprehension.

Not converting the key to uppercase.

Using a wrong function name for determinant.

The dictionary comprehension needs to create a dict, so dict is used. The keys from matrices.items() are strings like 'two', so key is used and converted to uppercase. The determinant function is det. The variable names in the comprehension must match the unpacking.

Practice

1. What does the determinant of a square matrix tell us in simple terms?

easy

A. If the matrix can be reversed or undone

B. The number of rows in the matrix

C. The sum of all elements in the matrix

D. The largest value in the matrix

Solution

1. Step 1: Understand determinant meaning

   The determinant helps us know if a matrix can be inverted or reversed.

2. Step 2: Relate to matrix properties

   If the determinant is zero, the matrix cannot be inverted; otherwise, it can.

3. Final Answer:

   If the matrix can be reversed or undone -> Option A

4. Quick Check:

   Determinant shows invertibility [OK]

Hint: Determinant zero means no inverse [OK]

Common Mistakes:

• Confusing determinant with matrix size
• Thinking determinant is sum of elements
• Assuming determinant gives max value

2. Which of the following is the correct way to import the determinant function from scipy?

easy

A. from scipy import determinant

B. from scipy.linalg import det

C. import scipy.det

D. import det from scipy.linalg

Solution

1. Step 1: Recall scipy.linalg module usage

   The determinant function is in scipy.linalg and is named det.

2. Step 2: Check correct import syntax

   Python import syntax for a function is: from module import function.

3. Final Answer:

   from scipy.linalg import det -> Option B

4. Quick Check:

   Correct import syntax for det [OK]

Hint: Use 'from scipy.linalg import det' to import [OK]

Common Mistakes:

• Using wrong module name
• Incorrect import syntax
• Trying to import non-existent names

3. What is the output of this code?

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

medium

A. 14.0

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 code output

   Code prints determinant rounded to 2 decimals, so output is 5.0.

3. Final Answer:

   5.0 -> Option D

4. Quick Check:

   Determinant = 5.0 [OK]

Hint: Det = ad - bc for 2x2 matrix [OK]

Common Mistakes:

• Mixing multiplication order
• Not rounding output
• Confusing matrix elements

4. Identify the error in this code snippet:

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

medium

A. Matrix B is not square, so det() will raise an error

B. Missing import for numpy

C. det() function is misspelled

D. No error, code runs fine

Solution

1. Step 1: Check matrix shape

   Matrix B has shape (2,3), which is not square.

2. Step 2: Understand det() requirements

   det() requires a square matrix; otherwise, it raises a LinAlgError.

3. Final Answer:

   Matrix B is not square, so det() will raise an error -> Option A

4. Quick Check:

   det() needs square matrix [OK]

Hint: Only square matrices have determinants [OK]

Common Mistakes:

• Ignoring matrix shape
• Assuming det works on any matrix
• Overlooking error messages

5. You have a 3x3 matrix:

M = np.array([[1, 2, 3], [0, 1, 4], [5, 6, 0]])

Using scipy.linalg.det, what is the determinant of M? Choose the closest value rounded to 2 decimals.

hard

A. -24.00

B. 31.00

C. 1.00

D. -79.00

Solution

1. Step 1: Calculate determinant manually

   Calculate determinant of M:
   det(M) = 1*(1*0 - 4*6) - 2*(0*0 - 4*5) + 3*(0*6 - 1*5)
   = 1*(0 - 24) - 2*(0 - 20) + 3*(0 - 5)
   = -24 + 40 - 15 = 1

2. Step 2: Confirm with scipy.linalg.det

   Using det(M) in code returns 1.0, rounded to 2 decimals is 1.00.

3. Final Answer:

   1.00 -> Option C

4. Quick Check:

   Determinant = 1.00 [OK]

Hint: Use cofactor expansion for 3x3 determinant [OK]

Common Mistakes:

• Wrong sign in cofactor terms
• Mixing row and column indices
• Forgetting to round result