Let's find the matrix [tex]\( A \)[/tex].
Given:
[tex]\[
A = \begin{pmatrix}
3 & 9 & 27 & 81 \\
1 & 1 & 1 & 1 \\
-2 & 4 & -8 & 16 \\
2 & 4 & 8 & 16
\end{pmatrix}
\][/tex]
Step-by-step breakdown of the matrix [tex]\( A \)[/tex]:
1. First Row:
[tex]\[
\begin{pmatrix}
3 & 9 & 27 & 81
\end{pmatrix}
\][/tex]
2. Second Row:
[tex]\[
\begin{pmatrix}
1 & 1 & 1 & 1
\end{pmatrix}
\][/tex]
3. Third Row:
[tex]\[
\begin{pmatrix}
-2 & 4 & -8 & 16
\end{pmatrix}
\][/tex]
4. Fourth Row:
[tex]\[
\begin{pmatrix}
2 & 4 & 8 & 16
\end{pmatrix}
\][/tex]
Combining these rows together gives us the matrix [tex]\( A \)[/tex]:
[tex]\[
A = \begin{pmatrix}
3 & 9 & 27 & 81 \\
1 & 1 & 1 & 1 \\
-2 & 4 & -8 & 16 \\
2 & 4 & 8 & 16
\end{pmatrix}
\][/tex]
So, the matrix [tex]\( A \)[/tex] is:
[tex]\[
A = \begin{pmatrix}
3 & 9 & 27 & 81 \\
1 & 1 & 1 & 1 \\
-2 & 4 & -8 & 16 \\
2 & 4 & 8 & 16
\end{pmatrix}
\][/tex]
This is the final form of matrix [tex]\( A \)[/tex].
