I have been studying Inner Product spaces for the past week and seem unable to grasp the concept. For instance, here is a sample problem from my textbook. I have the answer in the back, but I just can't seem to reach the same answer.
||f|| = ???
I keep coming up with sqrt(2/3), while the answer key states (sqrt(6))/3.
Please show me how they got their answer.
2006-12-22 03:58:33 · 6 answers · asked by frich_27 2 in Science & Mathematics ➔ Mathematics
You got the right answer already. sqrt(2/3) is (sqrt(6))/3. They just rationalized the denominator by multiplying by (sqrt(3))/(sqrt(3)) which is equal to 1.
2006-12-22 04:05:14 · answer #1 · answered by adrian b 3 · 4⤊ 0⤋
They are both the same answer. Your calculator will verify that. So will math. Start with your answer. Then multiply both numerator and denominator by √3.
√(2/3) = (√2)/(√3) = [(√2)(√3)]/[(√3)(√3)] = (√6)/3
2006-12-22 04:15:01 · answer #2 · answered by Northstar 7 · 0⤊ 1⤋
||f|| = sqrt
If f(x) = x, then
I must agree with you; the answer is sqrt(2/3). I think the book is wrong!
Sincerely,
açafrão341@yahoo.com
2006-12-22 04:05:59 · answer #3 · answered by acafrao341 5 · 0⤊ 2⤋
Yep same answer as other posters.
A hint when using book answers, if you don't agree, compare. Like the other poster said, try the decimals on a calculator. Once you see the decimals are equal you should end up going "Oh yeah"
2006-12-22 04:30:29 · answer #4 · answered by a_math_guy 5 · 0⤊ 1⤋
adrian's the big winner on this one.
sqrt(2/3)*[sqrt(3)/sqrt(3)] = sqrt(6)/3
2006-12-22 05:08:52 · answer #5 · answered by modulo_function 7 · 0⤊ 0⤋
(6)/2
2006-12-22 05:00:39 · answer #6 · answered by Anonymous · 0⤊ 0⤋