Write Python code (or modify code in 4.4 ) to do the following:\ Input into a variable

A

the matrix

([4.1,2.8],[9.7,6.7])

.\ Input into a variable

b

the vector

(4.1,9.7)

.\ Use the LU method to solve the linear system

Av=b

. Denote the solution you find by

v1

.\ Input into a variable

db

the vector

(0.01,0)

.\ Use the LU method to solve the linear system

Av=b+db

. Denote the solution you find by

v2

.\ Evaluate, in any norm you choose,

||v1-v2|(|

|)/(

|

|)

|v1||

and show that this relative change of the solution is bound from above by the quantity

k(A)*||db|(|

|)/(

|

|)

|b||

, where

k(A)

is the matrix conditioning.

Write Python code (or modify code in 4.4 ) to do the following: 1. Input into a variable A the matrix (4.19.72.86.7). 2. Input into a variable b the vector (4.1,9.7). 3. Use the LU method to solve the linear system Av=b. Denote the solution you find by v1. 4. Input into a variable db the vector (0.01,0). 5. Use the LU method to solve the linear system Av=b+db. Denote the solution you find by v2. 6. Evaluate, in any norm you choose, v1v2/v1 and show that this relative change of the solution is bound from above by the quantity k(A)db/b, where k(A) is the matrix conditioning