Describe a Turing machine that receives the encoding of a graph and decides whether the graph is a tree. To do this, think about how the input should be encoded $($hint: adjancency matrix$).$ Tackle the task in two steps.

$1.$ First, write a Turing machine that stops in qno if the input does not meet the criteria for an encoded graph.

$2.$ Then extend the Turing machine so that it also stops in qno if the input is not a tree and stops in qja if the input is a tree.

In this task, the transition function does not have to be specified in a table; a very precise verbal description is sufficient.