1. evaluate the following integral: \\(\\int \\cos x \\ln(\\sin x) dx\\)

Brief Explanations:

A matrix in row echelon form has leading entries (pivots) that are to the right of the pivot in the row above, and all zero rows are at the bottom. For it to not be in reduced row echelon form, at least one column with a pivot must have a non-zero entry above or below the pivot. We construct a 3x6 matrix meeting these criteria.

Answer:

$$\begin{bmatrix} 1 & 2 & 3 & 4 & 5 & 6 \ 0 & 1 & 2 & 3 & 4 & 5 \ 0 & 0 & 1 & 2 & 3 & 4 \end{bmatrix}$$