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Given the matrix

[tex]\[ A=\left(\begin{array}{cccc}
3 & 9 & 27 & 81 \\
1 & 1 & 1 & 1 \\
-2 & 4 & -8 & 16 \\
2 & 4 & 8 & 16
\end{array}\right) \][/tex]

Find the determinant of [tex]\(A\)[/tex].



Answer :

GinnyAnswer
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].

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