To find the element in row 1, column 1 of the matrix [tex]\(-3A + B\)[/tex], we will perform the following steps:
1. Multiply matrix [tex]\( A \)[/tex] by [tex]\(-3\)[/tex] to get [tex]\(-3A\)[/tex]:
[tex]\[
A = \begin{pmatrix}
7 & -7 \\
-4 & 0
\end{pmatrix}
\][/tex]
[tex]\[
-3A = -3 \cdot \begin{pmatrix}
7 & -7 \\
-4 & 0
\end{pmatrix} =
\begin{pmatrix}
-3 \cdot 7 & -3 \cdot (-7) \\
-3 \cdot (-4) & -3 \cdot 0
\end{pmatrix} =
\begin{pmatrix}
-21 & 21 \\
12 & 0
\end{pmatrix}
\][/tex]
2. Add matrix [tex]\( B \)[/tex] to [tex]\(-3A\)[/tex] to get [tex]\(-3A + B\)[/tex]:
[tex]\[
B = \begin{pmatrix}
2 & 5 \\
0 & -1
\end{pmatrix}
\][/tex]
[tex]\[
-3A + B = \begin{pmatrix}
-21 & 21 \\
12 & 0
\end{pmatrix} + \begin{pmatrix}
2 & 5 \\
0 & -1
\end{pmatrix} = \begin{pmatrix}
-21 + 2 & 21 + 5 \\
12 + 0 & 0 + (-1)
\end{pmatrix} =
\begin{pmatrix}
-19 & 26 \\
12 & -1
\end{pmatrix}
\][/tex]
3. Identify the element in row 1, column 1 of [tex]\(-3A + B\)[/tex]:
The element in row 1, column 1 of the resulting matrix [tex]\(-3A + B\)[/tex] is [tex]\(-19\)[/tex].
Therefore, the element in row 1, column 1 of [tex]\(-3A + B\)[/tex] is [tex]\(\boxed{-19}\)[/tex].
