9. Linear Systems II

Conditioning — Quiz

Test your understanding of conditioning with 5 practice questions.

Practice Questions

Question 1

In linear systems, what does conditioning primarily describe?

Question 2

A system is called ill-conditioned when it is true that

Question 3

For the matrix $A=\begin{pmatrix}2&0\\0&8\end{pmatrix}$, what is its condition number in the $2$-norm?

Question 4

What does $\kappa(A)=1$ indicate for a nonsingular matrix?

Question 5

If the relative perturbation in the data is $0.001$ and $\kappa(A)=200$, what worst-case relative error estimate is suggested for the solution?