Consider the system where b1 ≠ 0 and b2 ≠ 0. Its exact solution is...

Consider the system

where b₁ ≠ 0 and b₂ ≠ 0. Its exact solution is

a a. Let b₁ = 1 and b₂ = 2. Solve this system using naive Gaussian elimination with three-digit (rounded) arithmetic and compare with the exact solution x₁ = 1.00010 . . . and x₂ = 0.99989 9. . . .

a b. Repeat the preceding part after interchanging the order of the two equations.

a c. Find values of b₁ and b₂ in the original system so that naive Gaussian elimination does not give poor answers.