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watchmath
 5 years ago
Find the determinant of
\[\begin{pmatrix}a&b&b&\cdots&b\\b&a&b&\cdots&b\\b&b&a&\cdots&b\\\vdots&\vdots&\vdots&\quad&\vdots\\b&b&b&\cdots&a\end{pmatrix}_{n\times n}\]
watchmath
 5 years ago
Find the determinant of \[\begin{pmatrix}a&b&b&\cdots&b\\b&a&b&\cdots&b\\b&b&a&\cdots&b\\\vdots&\vdots&\vdots&\quad&\vdots\\b&b&b&\cdots&a\end{pmatrix}_{n\times n}\]

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Book says use the Leibniz formula...but that formula is tough.

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0@Anwar: If it is a \(2\times 2\) matrix, then the determinant is \(a^2b^2\). But we don't get that if we plug in \(n=2\) to your answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh you're right. This is right for n>2. It can be shown by mathematical induction.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I did it quickly, so it might not be right. I have to go now, I'll do it again when I am back.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Although my answer seems to be correct :D

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0The answer should be true for \(n\geq 1\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry, I made a mistake.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It has be something like for \(n=3; 3a(a^2b^2)\) and for \(n=4; 4a(3a(a^2b^2))\) I'll write the full solution when I come back. I just have to go for like 30 minutes or something.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here the form I came up with for \(n≥2\): \[{n! \over 2} a^{n2}(a^2b^2)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What's up satellite?!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i was hoping you could take a second to look at this my attempted answer to the fib question. i think he/she said something bigger than 25 , but i got 25

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0on the other hand i frequently make mistakes. and not just in my typesetting.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I could not find the mistake you made, if you did make one.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks another pair of eyes is always good. still it worries me that they said they got something larger than 25. i am not going to fret any more about it.
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