A3

Part of 1984 Putnam

Problems(1)

Source:

n

be a positive integer. Let

a,b,x

be real numbers, with

a \neq b

M_n

2n x 2n

(i,j)

m_{ij}

m_{ij}=x

i=j

m_{ij}=a

i \not= j

i+j

m_{ij}=b

i \not= j

i+j

is odd. For example

M_2=\begin{vmatrix}x& b& a & b\\ b& x & b &a\\ a & b& x & b\\ b & a & b & x \end{vmatrix}

\lim_{x\to\ 0} \frac{ det M_n}{ (x-a)^{(2n-2)} }

as a polynomial in

a,b

n

.
P.S. How write in latex

m_{ij}=...

with symbol for the system (because is multiform function?)

Putnamlinear algebramatrixlimitalgebrapolynomialLaTeX