Hi

can anyone help with the last 3 determinants( exc: 8,9,10)(Doh)

from this page

http://myweb.polyu.edu.hk/~majleung/...terminants.pdf

Thank you!

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- Feb 23rd 2010, 03:26 AMbenusDeterminants
Hi

can anyone help with the last 3 determinants( exc: 8,9,10)(Doh)

from this page

http://myweb.polyu.edu.hk/~majleung/...terminants.pdf

Thank you! - Feb 23rd 2010, 04:54 AMHallsofIvy
Look at the righthand side of each of those.

Do you have a theorem that says

$\displaystyle \left|\begin{array}{cccc}a_1+ x & x & \cdot\cdot\cdot & x \\ x & a_2+ x & \cdot\cdot\cdot & x\\ \cdot & \cdot & \cdot & \cdot \\x & x & \cdot\cdot\cdot a_n+ x\end{array}\right|$$\displaystyle = a_1a_2\cdot\cdot\cdot a_n+ (a_1+ a_2+ \cdot\cdot\cdot+ a_n)x$?

If not, could you prove it by induction on n?