To solve for [tex]\(2A - 3B\)[/tex], let's break down the computation step by step.
1. Define the matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[
A = \begin{pmatrix}
5 & -8 \\
3 & 0
\end{pmatrix}
\][/tex]
[tex]\[
B = \begin{pmatrix}
2 & -9 \\
1 & 0
\end{pmatrix}
\][/tex]
2. Calculate [tex]\(2A\)[/tex]:
[tex]\[
2A = 2 \cdot \begin{pmatrix}
5 & -8 \\
3 & 0
\end{pmatrix} = \begin{pmatrix}
2 \cdot 5 & 2 \cdot -8 \\
2 \cdot 3 & 2 \cdot 0
\end{pmatrix} = \begin{pmatrix}
10 & -16 \\
6 & 0
\end{pmatrix}
\][/tex]
3. Calculate [tex]\(3B\)[/tex]:
[tex]\[
3B = 3 \cdot \begin{pmatrix}
2 & -9 \\
1 & 0
\end{pmatrix} = \begin{pmatrix}
3 \cdot 2 & 3 \cdot -9 \\
3 \cdot 1 & 3 \cdot 0
\end{pmatrix} = \begin{pmatrix}
6 & -27 \\
3 & 0
\end{pmatrix}
\][/tex]
4. Calculate [tex]\(2A - 3B\)[/tex]:
[tex]\[
2A - 3B = \begin{pmatrix}
10 & -16 \\
6 & 0
\end{pmatrix} - \begin{pmatrix}
6 & -27 \\
3 & 0
\end{pmatrix} = \begin{pmatrix}
10 - 6 & -16 - (-27) \\
6 - 3 & 0 - 0
\end{pmatrix} = \begin{pmatrix}
4 & 11 \\
3 & 0
\end{pmatrix}
\][/tex]
Thus, the result of [tex]\(2A - 3B\)[/tex] is:
[tex]\[
\begin{pmatrix}
4 & 11 \\
3 & 0
\end{pmatrix}
\][/tex]
Therefore, the correct answer is:
A. [tex]\(\left[\begin{array}{cc}4 & 11 \\ 3 & 0\end{array}\right]\)[/tex]
