Matrix Problems Matrix Problems 5 Let A be a 3 X 3 matrix an

Matrix Problems:

Matrix Problems: 5. Let A be a 3 X 3 matrix, and its eigenvalues are Lambda1= -1, lambda2 = 4, lambda3 = 25. What is the condition number for A measured in l2-norm? A) -25. B)-4. C) 0. D) 25. 6. If a matrix A has large condition number, then the system Ax = b is ill-conditioned and hard to solve numerically. A) True B) False

Solution

5)

condition no = mod of (e_max/e_min) =|25/-1| =25 (D)

6)

True.

If the condition number is very large, then the matrix is said to be ill-conditioned. Practically, such a matrix is almost singular, and the computation of its inverse, or solution of a linear system of equations is prone to large numerical errors. A matrix that is not invertible has condition number equal to infinity.