Prove that the determinant of the matrix
is equal to .
Do I approach this with induction? where do I start?
emakarov is suggesting a row operation. Do you know how row operations on a matrix change the determinant?
If you swap two rows, you multiply the determinant by -1.
If you multiply a row by a constant, you multiply the determinant by that constant.
If you add a multiple of a row to another row (such as adding 1 times the last two to each other row) does not change the determinant.
Which of course is a diagonal matrix so the determinant is the product of the diagonal terms, however the last one is 0, which throws this off. What did I do wrong?
I can see that the first terms give you but where does the last come from?