To find the resulting vector matrix of the given matrix multiplication, we perform the following steps:
1. Identify the given matrix [tex]\(A\)[/tex] and vector [tex]\(B\)[/tex]:
[tex]\[
A = \begin{bmatrix}
6 & -5 \\
-3 & 4 \\
\end{bmatrix}
\][/tex]
[tex]\[
B = \begin{bmatrix}
-1 \\
3 \\
\end{bmatrix}
\][/tex]
2. Compute the first element [tex]\(a\)[/tex] of the resulting vector by multiplying the first row of matrix [tex]\(A\)[/tex] with vector [tex]\(B\)[/tex]:
[tex]\[
a = (6 \times -1) + (-5 \times 3)
\][/tex]
[tex]\[
a = -6 - 15
\][/tex]
[tex]\[
a = -21
\][/tex]
3. Compute the second element [tex]\(b\)[/tex] of the resulting vector by multiplying the second row of matrix [tex]\(A\)[/tex] with vector [tex]\(B\)[/tex]:
[tex]\[
b = (-3 \times -1) + (4 \times 3)
\][/tex]
[tex]\[
b = 3 + 12
\][/tex]
[tex]\[
b = 15
\][/tex]
So, the resulting vector matrix of the multiplication is:
[tex]\[
\begin{bmatrix}
-21 \\
15 \\
\end{bmatrix}
\][/tex]
Therefore, [tex]\(a = -21\)[/tex] and [tex]\(b = 15\)[/tex].
