To solve for the product [tex]\( BA \)[/tex] where
[tex]\[
B = \begin{pmatrix}
2 & 8 \\
6 & 3
\end{pmatrix}
\][/tex]
and
[tex]\[
A = \begin{pmatrix}
3 & 0 \\
2 & -1
\end{pmatrix}
\][/tex]
we need to perform matrix multiplication.
Given that the result of the matrix multiplication [tex]\( BA \)[/tex] is:
[tex]\[
BA = \begin{pmatrix}
22 & -8 \\
24 & -3
\end{pmatrix}
\][/tex]
Let's now match this result with the provided options:
A. [tex]\(\begin{pmatrix} 22 & -8 \\ 3 & -3 \end{pmatrix}\)[/tex]
B. [tex]\(\begin{pmatrix} 6.2 & 3 \\ 12.2 & -18 \end{pmatrix}\)[/tex]
C. [tex]\(\begin{pmatrix} 6 & 24 \\ 3.4 & 13 \end{pmatrix}\)[/tex]
D. [tex]\(\begin{pmatrix} 22 & -8 \\ 7.8 & -3 \end{pmatrix}\)[/tex]
None of these match the correct result exactly.
Given the provided choices, none of them correctly match the solution that we have for the matrix [tex]\( BA \)[/tex].
Hence, there appears to be an error in the provided answer choices. If forced to select the closest, we'd select [tex]\( B \)[/tex], which partially matches one element. But none fully match, suggesting a possible issue in the formulation of the options.
