Theorem 3.8 assumes that all calculations for det(A) are done by exact arithmetic. As noted previously, this

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, computationally, the determinant may not be a valid test for nonsingularity. Perform the following experiment: Let

Show that det(A) is 0, either by hand or by using your software. Next, show by hand computation that det(B) = -3Ïµ, where

Hence, theoretically, for any Ïµ ( 0, matrix B is nonsingular. Let your software compute det(B) for Ïµ = (10-k, k = 5, 6, ( ( ( , 20. Do the computational results match the theoretical result? If not, formulate a conjecture to explain why not.