Question

Calculate the second term in the cofactor expansion along the third row for the matrix
[[-3,-2,2,1],[-3,4,-1,2],[4,-3,2,-1],[-2,-3,2,1]]

Answer 1

is this what you mean?

\[\left[\begin{array} -3&-2&2&1\\ -3&4&-1&2\\ 4&-3&2&-1\\ -2&-3&2&1 \end{array}\right]\left[\begin{array} \ x_1 \\ x_2\\x_3\\x_4\end{array}\right]\]
\[4x_1\color{red}{-3}x_2+2x_3-x_4\]

or are we taking the determinant?

Answer 2

+-+ - get us to the second term in the third row

ignore the elements of the tird row and the second column, and generate the determinant of the submatrix of the rest of the elements

\[-\begin{vmatrix} -3&*&2&1\\-3&*&-1&2\\*&*&*&*\\-2&*&2&1 \end{vmatrix}\]
the stars can be ignored