Linear Algebra and Calculus DY0-001 Practice Questions (Page 3)

Questions 11–15

1. 11foundation · easy

   What is the rank of the following matrix? [[1, 2], [2, 4]]

   • A0
   • B1
   • C2
   • D3
   Reveal Solution Discussion Select an answer first
2. 12application · medium

   A data scientist is analyzing a covariance matrix for a set of features. The covariance matrix is given as [[4, 0], [0, 9]]. They want to understand the variance explained by the principal components. What are the eigenvalues of this matrix, and what do they represent?

   • AEigenvalues are 6.5 and 6.5; they represent the average variance across all components.
   • BEigenvalues are 2 and 3; they represent the standard deviations along the principal components.
   • CEigenvalues are 0 and 13; they represent the minimum and maximum variance.
   • DEigenvalues are 4 and 9; they represent the variance along the two principal component directions.
   Reveal Solution Discussion Select an answer first
4. 13foundation · easy

   What are the eigenvalues of the matrix [[2, 0], [0, 3]]?

   • A2 and 2
   • B2 and 3
   • C0 and 5
   • D1 and 6
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5. 14application · medium

   A machine learning engineer is tuning a model with a loss function L(a, b) = a^2 * b + e^(a*b). They need to compute the gradient with respect to a to update the parameter during gradient descent. What is ∂L/∂a?

   • A2*a*b + b * e^(a*b)
   • B2*a*b + a * e^(a*b)
   • C2*a*b + e^(a*b)
   • Da^2 + e^(a*b)
   Reveal Solution Discussion Select an answer first
6. 15foundation · easy

   What is the value of log_2(8)?

   • A8
   • B4
   • C3
   • D2
   Reveal Solution Discussion Select an answer first