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// EXAMPLE (PG 531)
// Consider the linear system
// 7*x1 + 10*x2 = b1
// 5*x1 + 7*x2 = b2
A = [7 10;5 7] // Coefficient matrix
inv(A) // Inverse matrix
// cond(A)1 // Condition matrix
norm(A,1)*norm(inv(A),1)
// cond(A)2 // Condition matrix
norm(A,2)*norm(inv(A),2)
// These condition numbers all suggest that the above system
// may be sensitive to changes in the right side b.
// Consider the particular case
b = [1 0.7]'; // Right hand matrix
x = A\b; // Solution matrix
// Solution matrix
x1 = x(1,:)
x2 = x(2,:)
// For the perturbed system, we solve for:
b = [1.01 0.69]'; // Right hand matrix
x = A\b; // Solution matrix
// Solution matrix
x1 = x(1,:)
x2 = x(2,:)
// The relative changes in x are quite large when compared with
// the size of the relative changes in the right side b.
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