Exercise 3: Mapping Real Tools to Linear Algebra Topics — Possible Solution
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(A) CSS transform: matrix(a, b, c, d, e, f) — MATRICES AS
TRANSFORMATIONS (CHAPTER 4-5)
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This CSS rule literally names itself after the concept - the six
numbers passed to matrix() are the entries of a 2D transformation
matrix, which is then applied to every point of the element being
styled to rotate, scale, skew, or translate it.

(B) FITTING A STRAIGHT TREND LINE THROUGH A SCATTER PLOT — SYSTEMS OF
LINEAR EQUATIONS (CHAPTER 6)
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Finding the slope and intercept that best fit a set of data points
means solving for two unknowns using the data points' own
constraints - exactly a system of linear equations, solved here in
its "best fit" (least-squares) form rather than for an exact
solution.

(C) REDUCING 50 COLUMNS DOWN TO THE 2-3 DIRECTIONS CAPTURING MOST
VARIATION — EIGENVALUES & EIGENVECTORS (CHAPTER 9)
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This is a direct description of Principal Component Analysis (PCA).
The "directions that capture the most variation" in a dataset are
literally the eigenvectors of the dataset's covariance matrix, ranked
by the size of their corresponding eigenvalues - exactly this
chapter's own forward reference to Chapter 9.

WHY THIS WORKS AS AN ANSWER
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Each artifact is matched to its topic by identifying the specific
operation actually being performed - applying a transformation matrix,
solving for unknowns using linear constraints, or finding the
dominant directions of variation via eigenvectors - rather than by
surface-level keyword matching alone.