To solve this problem, we need to recognize the property that matrices [tex]\( C \)[/tex] and [tex]\( D \)[/tex] are equal. When two matrices are equal, their corresponding entries are also equal. This means that for any element [tex]\( c_{ij} \)[/tex] in matrix [tex]\( C \)[/tex], it must be equal to the corresponding element [tex]\( d_{ij} \)[/tex] in matrix [tex]\( D \)[/tex].
Given matrix [tex]\( C \)[/tex]:
[tex]\[
C = \left[
\begin{array}{cccc}
4 & -3 & 8 & 9.2 \\
1.2 & -6 & 5 & 1 \\
6 & 0 & -7 & 23
\end{array}
\right]
\][/tex]
And the corresponding matrix [tex]\( D \)[/tex]:
[tex]\[
D = \left[
\begin{array}{cccc}
d_{11} & d_{12} & d_{13} & d_{14} \\
d_{21} & d_{22} & d_{23} & d_{24} \\
d_{31} & d_{32} & d_{33} & d_{34}
\end{array}
\right]
\][/tex]
We are asked to find the value of [tex]\( d_{33} \)[/tex], which is the element in the 3rd row and 3rd column of matrix [tex]\( D \)[/tex].
Looking at the same position in matrix [tex]\( C \)[/tex], the element is:
[tex]\[ C[2][2] = -7 \][/tex]
Since [tex]\( C \)[/tex] and [tex]\( D \)[/tex] are equal, the value of [tex]\( d_{33} \)[/tex] will be the same as the value at [tex]\( C[2][2] \)[/tex].
Hence, the value of [tex]\( d_{33} \)[/tex] is:
[tex]\[
d_{33} = -7
\][/tex]
Therefore, the correct answer is:
[tex]\[ -7 \][/tex]
