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# Condition Number watch

1. Had this question appear on a practice exam last week:
The matrix A has condition number K(A)=2. What is K(3A)?

Now in our notes I cannot see anything that lists properties of condition numbers or anything. As such, both myself and several others calculated it to be 18 as we thought since ||A||.||A^-1|| = 2, by the question, then ||3A||.||3A^-1|| = 9*(||A||.||A^-1||) which would imply 9*2 = 18.
However according to the answers K(3A)=2, still. Can someone please explain why/how this is achieved?

Thanks
2. (Original post by orionmoo)
Had this question appear on a practice exam last week:
The matrix A has condition number K(A)=2. What is K(3A)?

Now in our notes I cannot see anything that lists properties of condition numbers or anything. As such, both myself and several others calculated it to be 18 as we thought since ||A||.||A^-1|| = 2, by the question, then ||3A||.||3A^-1|| = 9*(||A||.||A^-1||) which would imply 9*2 = 18.
However according to the answers K(3A)=2, still. Can someone please explain why/how this is achieved?

Thanks
I'd have thought

but I'm no expert.
3. Hmmmm well that would make sense lol. To me though, it isn't clear based on my notes whether it's 3*A^-1 or (3A)^-1... and clearly not to the others i spoke to! hmm
4. (Original post by orionmoo)
Hmmmm well that would make sense lol. To me though, it isn't clear based on my notes whether it's 3*A^-1 or (3A)^-1... and clearly not to the others i spoke to! hmm
If you think of it as K(Y) = ||Y||.||Y^-1||

and then let Y=3A, the only possible interpretation it seems, to me, is:

K(3A) = ||3A||.||(3A)^-1||

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