Determinant problem/Solution

A solution: The approach used here is to use Gaussian Elimination. Divide the top row by :

Anticipate addition of rows along the second column:

This should become the leading element of the second row.

Anticipate addition of rows along the third and latter columns:

This should become the trailing elements of the second row.

Add the first row to the second row and the rows below it:

Divide the second row by :

Anticipate addition along third column:

This should become the new leading element of the third row.

Anticipate addition along fourth and latter columns:

This should become the trailing elements of the third row.

Add the second row to the rows below it:

Divide the third row by :

Anticipate addition along the fourth column:

This should become the leading element of the fourth row.

Anticipate addition along the fifth and latter columns:

This should become the trailing elements of the fourth row.

Add the third row to the rows below it:

Divide the fourth row by :

Add fourth row to rows below it:

For purposes of calculating a determinant, the non-diagonal elements of an upper-triangular matrix do not matter. By induction the equation ends up looking thus:

The determinant of the upper triangular matrix equals the product of its diagonal elements:

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