Exercise 2: Linear Algebra Beyond Machine Learning — Possible Solution
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THE CLAIM BEING CHALLENGED
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The colleague's claim is that linear algebra only matters for machine
learning work. This chapter's own five-connections table shows at
least two clear counterexamples where linear algebra is doing real
work with no ML involved at all.

COUNTEREXAMPLE 1: GRAPHICS AND DESIGN TOOL TRANSFORMS
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Every time an object is rotated, scaled, or skewed in a tool like
Blender, Figma, or a vector graphics editor, that operation is a
matrix being applied to every vector (point) making up the object.
CSS's own transform: matrix(a, b, c, d, e, f) rule is the exact same
idea, applied directly in a browser with zero machine learning
anywhere nearby.

COUNTEREXAMPLE 2: FITTING A TREND LINE THROUGH DATA
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Finding the best-fit straight line through a scatter plot of data
points - ordinary linear regression - is solved by setting up and
solving a system of linear equations for the line's slope and
intercept. This is a classic, decades-old statistics technique that
predates modern machine learning entirely, even though the same
underlying linear algebra later got reused inside ML tooling too.

WHY THIS WORKS AS AN ANSWER
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It directly challenges the colleague's premise using two of this
chapter's own five connections - matrix transformations in graphics
tools and linear systems in curve fitting - both of which are
genuinely standalone use cases for linear algebra with no dependency
on machine learning at all, rather than simply restating that ML also
uses linear algebra (which the colleague already believes).