To determine which matrix is equal to [tex]\(\left[\begin{array}{cc}3 & 2 \\ -5 & 9\end{array}\right]\)[/tex], let's compare each option provided:
1. The first option is [tex]\(\left[\begin{array}{llll} 3 & 2 & -5 & 9 \end{array}\right]\)[/tex]. This represents a single row matrix with four elements, which is not the same as having two rows and two columns. Therefore, this option is incorrect.
2. The second option is [tex]\(\left[\begin{array}{llll} 3 & -5 & 2 & 9 \end{array}\right]\)[/tex]. This also represents a single row matrix with four elements. Again, this is not the same format as the given 2x2 matrix. Therefore, this option is incorrect.
3. The third option is [tex]\(\left[\begin{array}{cc} 3 & 2 \\ -5 & 9 \end{array}\right]\)[/tex]. This matrix has the same number of rows and columns (2x2) and identical elements arranged in the same positions as the given matrix. Therefore, this option is correct.
4. The fourth option is [tex]\(\left[\begin{array}{cc} 3 & -5 \\ 2 & 9 \end{array}\right]\)[/tex]. This represents a 2x2 matrix, but the elements are arranged differently from the given matrix. Therefore, this option is incorrect.
Based on the comparisons, the matrix that is equal to [tex]\(\left[\begin{array}{cc}3 & 2 \\ -5 & 9\end{array}\right]\)[/tex] is the third option:
[tex]\[
\boxed{4}
\][/tex]
