Lecture 2

Question 1

When is a matrix nonsingular?

Name 4

Answer 1

Question 2

If A is singular what does this imply for Ax = b?

Answer 2

Question 3

What is Gaussian elimination?

Answer 3

Question 4

Why is LU decomposition useful?

Answer 4

Question 5

When is a matrix upper triangular?

Answer 5

Question 6

How to solve a upper triangular system?

Answer 6

Question 7

What is a lower triangular system?

Answer 7

Question 8

How to solve a lower triangular system?

Answer 8

Question 9

What is the idea behind LU decomposition?

Answer 9

Question 10

How do you solve Ax = b, using LU decomposition?

Answer 10

Question 11

What are elimination matrices, how do they relate to LU decomposition?

Answer 11

Question 12

What is the algorithm for LU decomposition by Gaussian elimination?

Answer 12

Question 13

What is the cost of LU decomposition by Gaussian elimination?

Answer 13

Question 14

What is the definition of a norm function?

Answer 14

Question 15

What are some important norm functions? What is the general formula?

Answer 15

Question 16

What is the norm of a matrix?

Answer 16

Question 17

What properties do matrix norms follow?

Answer 17

Question 18

What is the definition of a condition number of a matrix?

Answer 18

Question 19

What does the condition number represent?

Answer 19

Question 20

What are the four properties of a condition matrix?

Answer 20