I'm proving the statement
" det A where A = [ $a_{ij}$ ] $\in$ M$_n$(R) is defined as $a_{ij}$ = 0 when n+1 <= i+j "
and it should be proved by mathematical induction.
I know the answer since the last row of A is row of zeros in any number n, so det A is 0
The problem is that I have no idea how to solve with mathematical induction..
If I approach with mathematical induction,
Starting with n = 1) A = [0] so det A = 0
For inductive step, when n = k , let det A = 0.
then, when n = k + 1, and I should use the assumption that det A = 0 when n is k to show det A is 0 when n = k+1. At this point I have two questions.
First is I don't know how to approach inductive step.
Second is question about mathematical induction. Should I always solve inductive step from the assumption that it holds when n = k , although the situation n = k+1 can be proved without the assumption.
Thanks in advance.