- #1

erok81

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- 0

## Homework Statement

Consider the n x n determinant in which each entry on the main diagonal is a 2, each entry on the two adjacent diagonals is a 1, and every other entry is a zero.

Expand along the first row to show that B_n=2B_n-1 - B_n-2

## Homework Equations

n/a

## The Attempt at a Solution

I drew out a matrix, B_n...see my crossed out example. I am not sure how to type out a matrix using latex.

Also in my image you can see where I started the cofactor expansion along row 1. After a few entries, I realized this isn't even close to correct, so I stopped.

Now I am at a loss of how to proceed. We got some guidance from the professor, but I don't quite understand still. I've included his comments below.

Write out determinant B_n on paper using "..." notation. At least six (6) columns.

should be written, to give enough detail. Then use cofactor expansion along row 1

to produce 2 determinants of order n-1. Finally, use column 1 cofactor expansion

on the second determinant to produce a determinant of order n-2. All of this can

fit one one sheet of paper

Any direction would be appreciated.