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Consider solving Ax = b. we have two approximate solutions computed solution (x)...*x with a squiggly line on top of it* and error vector (x)...*x with a carrot symbol on top of it* as follows.  A = ( 0.780 0.563 0.913 0.659 ) b = （ 0.217 0.254 ） computed solution x =  ( 0.999 -1.001 ) x( with carrot on top) =  0.341 -0.097 The exact solution is x = [1,-1]^T. Compute the error       error vector e = computed solution (x) -x and    carrot e =  carrot x - x  and the residual vectors r = Ax(with squiggly line on top) - b and carrot r = Ax(carrot on top) - b . discuss the implication of this example

Consider solving Ax = b. we have two approximate solutions computed solution (x)...*x with a squiggly line on top of it* and error vector (x)...*x with a carrot symbol on top of it* as follows.  A = ( 0.780 0.563 0.913 0.659 ) b = （ 0.217 0.254 ） computed solution x =  ( 0.999 -1.001 ) x( with carrot on top) =  0.341 -0.097 The exact solution is x = [1,-1]^T. Compute the error       error vector e = computed solution (x) -x and    carrot e =  carrot x - x  and the residual vectors r = Ax(with squiggly line on top) - b and carrot r = Ax(carrot on top) - b . discuss the implication of this example

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider solving Ax = b. we have two approximate solutions computed solution (x)...*x with a squiggly line on top of it* and error vector (x)...*x with a carrot symbol on top of it* as follows. 

A = (

0.780 0.563
0.913 0.659

)

b = （

0.217
0.254

）

computed solution x = 

(

0.999
-1.001

)

x( with carrot on top) = 

0.341
-0.097

The exact solution is x = [1,-1]^T. Compute the error       error vector e = computed solution (x) -x and    carrot e =  carrot x - x  and the residual vectors r = Ax(with squiggly line on top) - b and carrot r = Ax(carrot on top) - b . discuss the implication of this example

Expert Solution
Step 1

Given that

A=0.7800.5630.9130.659b=0.2170.254x~=0.999-1.001x^=0.341-0.097

and the exact solution x=1-1

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