Why linear algebra matters in NumPy - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 2x2 matrix using numpy.

NumPy

import numpy as np
matrix = np.array([1])
print(matrix)

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

A[1, 2, 3, 4]

B[[1, 2], 3, 4]

C[[1, 2, 3], [4, 5, 6]]

D[[1, 2], [3, 4]]

Attempts:

3 left

💡 Hint

Common Mistakes

Passing a flat list instead of a list of lists.

Using uneven inner lists causing shape errors.

The correct way to create a 2x2 matrix is by passing a list of lists representing rows.

2fill in blank

medium

Complete the code to calculate the dot product of two vectors using numpy.

NumPy

import numpy as np
v1 = np.array([1, 2, 3])
v2 = np.array([4, 5, 6])
dot_product = np.[1](v1, v2)
print(dot_product)

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

Adot

Badd

Ccross

Dmultiply

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiply which returns element-wise product.

Using cross which calculates cross product, not dot product.

The np.dot function calculates the dot product of two vectors.

3fill in blank

hard

Fix the error in the code to compute the inverse of a matrix using numpy.

NumPy

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

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

Ainversed

Binverse

Cinv

Dinvert

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect function names like 'inverse' or 'invert'.

Trying to use non-existent functions causing AttributeError.

The correct numpy function to compute matrix inverse is np.linalg.inv.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if the length is greater than 3.

NumPy

words = ['data', 'science', 'is', 'fun']
lengths = { [1] : len([2]) for [1] in words if len([1]) > 3 }
print(lengths)

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

Aword

Bwords

Cw

Dlen

Attempts:

3 left

💡 Hint

Common Mistakes

Using the list name instead of the loop variable inside len().

Using different variable names inconsistently.

We use the variable 'word' to iterate over 'words' and map each word to its length if length > 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths only if length is greater than 2.

NumPy

words = ['AI', 'ML', 'Data', 'Code']
result = { [1] : [2] for [3] in words if len([3]) > 2 }
print(result)

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

Aword.upper()

Blen(word)

Cword

Dwords

Attempts:

3 left

💡 Hint

Common Mistakes

Using the list name instead of the loop variable.

Not applying upper() to the key.

Using inconsistent variable names.

The comprehension uses 'word' as the loop variable, maps word.upper() to len(word) if length > 2.

Practice

1.

Why is linear algebra important in data science when using numpy?

easy

A. It replaces the need for any programming language.

B. It is used only for creating visualizations.

C. It helps handle and transform large sets of numbers efficiently.

D. It is only useful for text data processing.

Solution

1. Step 1: Understand the role of linear algebra

   Linear algebra allows us to work with vectors and matrices, which represent many numbers at once.

2. Step 2: Connect to numpy's purpose

   NumPy uses linear algebra to efficiently perform operations on large numerical data sets.

3. Final Answer:

   It helps handle and transform large sets of numbers efficiently. -> Option C

4. Quick Check:

   Linear algebra = efficient number handling [OK]

Hint: Linear algebra = fast math with many numbers [OK]

Common Mistakes:

• Thinking linear algebra is only for visuals
• Believing it replaces programming
• Assuming it only works with text

2.

Which of the following is the correct way to create a 2x2 matrix using numpy?

import numpy as np
matrix = ?

easy

A. np.array([[1, 2], 3, 4])

B. np.array([[1, 2], [3, 4]])

C. np.array(1, 2, 3, 4)

D. np.matrix([1, 2, 3, 4])

Solution

1. Step 1: Recall numpy array syntax for matrices

   A 2x2 matrix requires a list of lists, each inner list is a row.

2. Step 2: Check each option's structure

   np.array([[1, 2], [3, 4]]) uses nested lists correctly; others do not form a proper 2x2 matrix.

3. Final Answer:

   np.array([[1, 2], [3, 4]]) -> Option B

4. Quick Check:

   Nested lists = matrix shape [OK]

Hint: Use nested lists for matrix shape [OK]

Common Mistakes:

• Using flat lists instead of nested
• Missing brackets around rows
• Confusing np.matrix with np.array

3.

What is the output of this code?

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[2, 0], [1, 2]])
result = np.dot(A, B)
print(result)

medium

A. [[1 2]
[3 4]]

B. [[2 0]
[1 2]]

C. [[3 4]
[4 6]]

D. [[4 4]
[10 8]]

Solution

1. Step 1: Understand matrix multiplication with np.dot

   np.dot multiplies matrices by summing products of rows and columns.

2. Step 2: Calculate each element of result

   First row, first column: 1*2 + 2*1 = 4; first row, second column: 1*0 + 2*2 = 4; second row, first column: 3*2 + 4*1 = 10; second row, second column: 3*0 + 4*2 = 8.

3. Final Answer:

   [[4 4] [10 8]] -> Option D

4. Quick Check:

   Matrix multiplication = [[4 4], [10 8]] [OK]

Hint: Multiply rows by columns, sum products [OK]

Common Mistakes:

• Adding matrices instead of multiplying
• Confusing element-wise with dot product
• Mixing up row and column indices

4.

Find the error in this code snippet that tries to multiply two matrices:

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([[7, 8], [9, 10]])
result = np.dot(A, B)
print(result)

medium

A. Matrix dimensions do not align for multiplication.

B. np.dot is not the correct function for multiplication.

C. Arrays A and B must be the same shape.

D. The print statement syntax is incorrect.

Solution

1. Step 1: Check shapes of matrices A and B

   A is 2x3, B is 2x2; for multiplication, columns of A must equal rows of B.

2. Step 2: Identify mismatch

   Since A has 3 columns and B has 2 rows, multiplication is not possible.

3. Final Answer:

   Matrix dimensions do not align for multiplication. -> Option A

4. Quick Check:

   Columns A != Rows B = Error [OK]

Hint: Check matrix shapes before multiplying [OK]

Common Mistakes:

• Ignoring shape mismatch
• Using wrong function for multiplication
• Assuming same shape needed for dot

5.

You have a dataset with 3 features and 4 samples stored as a 4x3 matrix. You want to center the data by subtracting the mean of each feature. Which numpy operation correctly achieves this?

import numpy as np
data = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
# What next?

hard

A. data - np.mean(data, axis=0)

B. data - np.mean(data, axis=1)

C. np.mean(data, axis=0) - data

D. np.mean(data, axis=1) - data

Solution

1. Step 1: Understand data shape and centering

   Data shape is 4 samples x 3 features; centering means subtracting feature means from each sample.

2. Step 2: Calculate mean along correct axis

   Axis=0 computes mean for each feature (column), which is needed to center features.

3. Step 3: Subtract feature means from data

   Subtracting np.mean(data, axis=0) from data centers each feature.

4. Final Answer:

   data - np.mean(data, axis=0) -> Option A

5. Quick Check:

   Center features by subtracting column means [OK]

Hint: Subtract mean along columns (axis=0) to center features [OK]

Common Mistakes:

• Using axis=1 subtracts row means, not features
• Subtracting data from mean reverses centering
• Confusing samples and features axes