Exercise 3: Why np.linalg.solve Sometimes Raises LinAlgError — Possible Solution
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WHAT PROPERTY OF A CAUSES THE CRASH
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np.linalg.solve raises a LinAlgError specifically when the coefficient
matrix A is singular - per this chapter's own forward reference to
Chapter 7, this means A has a determinant of exactly zero. A zero
determinant is precisely the signal, established in this chapter, that
the system A x = b does not have a single unique solution: it either
has no solution at all (an inconsistent system, like this chapter's
own [0, 0 | 3] example) or infinitely many (a dependent system, like
this chapter's own [0, 0 | 0] example). Since a teammate's code is
looping over "many different systems," it's very plausible that at
least one of those systems happens to have a coefficient matrix that
is singular - two of its equations might be scaled copies of each
other, or otherwise not genuinely independent.

WHY THIS IS BETTER THAN A SILENT WRONG ANSWER
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If np.linalg.solve instead tried to force out some numbers even for a
singular A - rather than raising an error - the result would be
mathematically meaningless: there either isn't a real answer to
report (the no-solution case) or there are infinitely many equally
valid answers and picking just one arbitrarily would misrepresent the
true situation (the infinite-solutions case). A crash is loud and
immediately visible in a test run or in production logs, which forces
the actual problem (a genuinely singular system somewhere in the
input data) to be investigated and fixed. A silently wrong number, by
contrast, would look like a completely ordinary, trustworthy result -
and could propagate through the rest of the program producing
incorrect downstream behavior with no error anywhere to point back to
the actual cause.

WHY THIS WORKS AS AN ANSWER
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It identifies the exact mathematical property (a zero determinant /
singular matrix) that this chapter's own forward reference connects
directly to the no-solution and infinite-solution cases already
covered, and argues for the crash being preferable using this
chapter's own established fact that neither of those two cases has a
single correct numeric answer to silently return.