Question - Determinants of Matrices with Variable Elements

\text{Let's calculate the determinant of the first visible matrix:}

\begin{vmatrix} a-1 & 3 & 5 \\ -1 & 3-5 & 5 \\ 1 & 3 & 5 \end{vmatrix}

\text{Expanding along the first column:}

(a-1)\begin{vmatrix} 3-5 & 5 \\ 3 & 5 \end{vmatrix} -(-1)\begin{vmatrix} -1 & 5 \\ 1 & 5 \end{vmatrix} + 1\begin{vmatrix} -1 & 3-5 \\ 1 & 3 \end{vmatrix}

=(a-1)((3-5)(5)-5(3)) -(-1)((-1)(5)-5(1)) + (1)((-1)(3)-3(3-5))

=(a-1)(-10+15) -(-1)(-5) + (1)(-3+6)

=(a-1)(5) -5 + 3

=5a-5 -5 +3

=5a-7

\text{Without more context or additional operations indicated for the other matrices, the calculation of their determinants isn't completed in the image.}