To determine which matrix from the given list is equal to [tex]\(\left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right]\)[/tex], I'll compare each option to the given matrix:
1. Option 1: [tex]\(\left[\begin{array}{cccc}3 & 2 & -5 & 9\end{array}\right]\)[/tex]
This option is a 1x4 matrix. It does not match the structure (2x2) of the given matrix. Therefore, it is not equal to the given matrix.
2. Option 2: [tex]\(\left[\begin{array}{cccc}3 & -5 & 2 & 9\end{array}\right]\)[/tex]
This option is also a 1x4 matrix. It again does not match the structure (2x2) of the given matrix. Therefore, it is also not equal to the given matrix.
3. Option 3: [tex]\(\left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right]\)[/tex]
This option is a 2x2 matrix. When we compare each corresponding element to the given matrix:
[tex]\[
\left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right] = \left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right]
\][/tex]
Every element matches. Therefore, this option is identical to the given matrix.
4. Option 4: [tex]\(\left[\begin{array}{cc}3 & -5 \\ 2 & 9\end{array}\right]\)[/tex]
This option is a 2x2 matrix. When we compare each corresponding element to the given matrix:
[tex]\[
\left[\begin{array}{cc}3 & -5 \\ 2 & 9\end{array}\right] \neq \left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right]
\][/tex]
There are differences in the elements, making this matrix not equal to the given matrix.
Therefore, the correct answer is Option 3: [tex]\(\left[\begin{array}{cc}3 & 2 \\ -5 & 8\end{array}\right]\)[/tex].
