Determinants

Quote:

Originally Posted by benus

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!

Look at the righthand side of each of those.
Do you have a theorem that says
$\left|\begin{array}{cccc}a_1+ x & x & \cdot\cdot\cdot & x \\ x & a_2+ x & \cdot\cdot\cdot & x\\ \cdot & \cdot & \cdot & \cdot \\x & x & \cdot\cdot\cdot a_n+ x\end{array}\right|$ $= a_1a_2\cdot\cdot\cdot a_n+ (a_1+ a_2+ \cdot\cdot\cdot+ a_n)x$ ?

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