To determine the element in [tex]\( M_{3,1} \)[/tex] of the given matrix [tex]\( M \)[/tex], let's break down the task step-by-step:
Given matrix [tex]\( M \)[/tex] is:
[tex]\[
\begin{pmatrix}
-49 & 12 & -14 & -41 \\
-35 & 34 & 37 & -19 \\
-34 & 49 & -10 & 32
\end{pmatrix}
\][/tex]
The notation [tex]\( M_{3,1} \)[/tex] refers to the element in the 3rd row and the 1st column of the matrix.
1. Identify the 3rd row of the matrix:
[tex]\[
\begin{pmatrix}
-34 & 49 & -10 & 32
\end{pmatrix}
\][/tex]
2. Identify the 1st element in this row, which corresponds to the 1st column:
[tex]\[
-34
\][/tex]
Thus, the element [tex]\( M_{3,1} \)[/tex] is:
[tex]\[
\boxed{-34}
\][/tex]
