Condition Number and Significant Digits

[DODGEVIPER13]

Homework Statement

IF A is nxn matrix, and k(A)=||A||||A^-1|| then a large k(A) means the solution has more significant digits than is k(A) were small true or false?

Homework Equations

The Attempt at a Solution

Well k(A) is defined as 10^(k) right so the larger the condition number the more significant digits that you shouldn't trust. So if I had 10^(16) I would have approximatley 16 sig figs that I shouldn't use. Therefore I would think the answer is true if condition number is large then there will be more significant digits just not usable ones right?

 

[DODGEVIPER13]

I get that the small the k(A) the more reliable a solution is meaning it would have to have an a good amount of sig figs such that it is accurate so maybe it is false hmmm I don't know?

 

[The Electrician]

Look here:

http://en.wikipedia.org/wiki/Condition_number

under the subheading "Matrices"

 

[DODGEVIPER13]

Ok, I will give that a look.

 

[DODGEVIPER13]

So it is saying that the higher the condition number the larger the error which is what I thought. So I guess what I am supposed to take from this is that the smaller the condition number the more precise the solution, however this problem specifies significant digits not precision so I am going to go with True.