It is possible to construct a binary tree uniquely whose pre-order and post-order traversals are given.

If the no of leaves in a tree is not a power of 2,then the tree is not a binary tree.

(a) Solve the recurrence equations
$$\,\,\,\,\,\,\,\,\,T\left( n \right) = T\left( {n - 1} \right) + n$$
$$\,\,\,\,\,\,\,\,\,T\left( 1 \right) = 1T$$
(b) What is the generating function?
$$\,\,\,\,\,\,\,\,\,G\left( z \right)$$ for the sequence of Fibonacci numbers?

A square matrix is singular whenever: