Question: Theorem 3.8 assumes that all calculations for det(A) are done by exact arithmetic. As noted previously, this is usually not the case in software. Hence,
Theorem 3.8 assumes that all calculations for det(A) are done by exact arithmetic. As noted previously, this is usually not the case in software. Hence, computationally, the determinant may not be a valid test for nonsingularity. Perform the following experiment: Let
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Show that det(A) is 0, either by hand or by using your software. Next, show by hand computation that det(B) = -3ϵ, where
-2.png)
Hence, theoretically, for any ϵ ( 0, matrix B is nonsingular. Let your software compute det(B) for ϵ = (10-k, k = 5, 6, ( ( ( , 20. Do the computational results match the theoretical result? If not, formulate a conjecture to explain why not.
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