Finding minor of the matrix

Question

Given the following matrix: $$\begin{pmatrix} 3 & 2 & 1 & 5 \\ 8 & 5 & 8 & t \\ 2 & 1 & 6 & 6 \end{pmatrix} $$ I am looking for the matrix rank depending on the parameter t. I have the information that minor formed by last three columns is equal to $11(16-t)$. Thus for $t\ne 16 $, $r(A)=3$. How this minor was calculated also i am not sure wheter i fully understand the definition of minor.

Answer 1

as i said in the comment, we can throw away the first column. we can compute the rank of $\pmatrix{2&1&5\\5&8&t\\1&6&6}\to \pmatrix{1&6&6\\2&1&5\\5&8&t} \to \pmatrix{1&6&6\\0&-11&-7\\0&-22&t-30} \to \pmatrix{1&6&6\\0&-11&-7\\0&0&t-16} $

so the rank of the original matrix if $ 3$ if and only if $t \neq 16$ and is $2$ otherwise.