To multiply the matrix [tex]\( \left[\begin{array}{cc} 6 & -1 \\ -4 & 3 \end{array}\right] \)[/tex] by the vector [tex]\( \left[\begin{array}{c} -5 \\ 4 \end{array}\right] \)[/tex]:
1. Multiply the first row of the matrix by the vector:
[tex]\[
6 \times (-5) + (-1) \times 4 = -30 - 4 = -34
\][/tex]
2. Multiply the second row of the matrix by the vector:
[tex]\[
-4 \times (-5) + 3 \times 4 = 20 + 12 = 32
\][/tex]
Thus, the resulting vector is:
[tex]\[
\left[\begin{array}{c} -34 \\ 32 \end{array}\right]
\][/tex]
Among the given choices, the correct answer is:
E. [tex]\(\left[\begin{array}{c} -34 \\ 32 \end{array}\right]\)[/tex]
