# Condition Number and Significant Digits

1. May 3, 2014

### DODGEVIPER13

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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 shouldnt trust. So if I had 10^(16) I would have approximatley 16 sig figs that I shouldnt 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?

2. May 3, 2014

### 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 dont know?

3. May 4, 2014

4. May 4, 2014

### DODGEVIPER13

Ok, I will give that a look.

5. May 4, 2014

### 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 gonna go with True.