A Python data pipeline has two steps. The first performs fast, vectorized mathematical operations on large multidimensional numeric arrays. The second trains a classification model on the prepared data and evaluates it with cross-validation. Which libraries best match these two steps?

NumPy is the foundational Python library for numerical computing. It provides the n-dimensional array type and vectorized operations, linear algebra and mathematical functions that run in compiled code, making it the right tool for fast math on large multidimensional numeric arrays. scikit-learn is the standard Python machine learning library; it supplies classification, regression and clustering algorithms behind a consistent fit and predict interface, along with model selection tools such as cross-validation, so it fits the training and evaluation step. scikit-learn itself uses NumPy arrays as input. Swapping the two misassigns their roles: scikit-learn is not a general array math library, and NumPy has no model training or cross-validation features. pandas could handle tabular preparation, but the first step is about multidimensional numeric arrays, which is NumPy's purpose, and Tidyverse is a set of R packages for data wrangling, not a Python model training library. Tidyverse cannot be used for array math in a Python pipeline, and MATLAB is a separate commercial computing environment with its own language rather than a Python library. Exam caveat: the DataSys+ objectives list NumPy, pandas, scikit-learn, Tidyverse and MATLAB as data manipulation tools, so expect questions that map each to its language and role. Operational check: confirm both libraries are pinned in the pipeline's dependency file and that the training step logs its cross-validation scores.