4) $$ \left[\begin{array}{cc}-2 & 4 \ -5 & -5\end{array} ight] \cdot\left[\begin{array}{l}4 \ 5\end{array} ight] $$

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4) $$ \left[\begin{array}{cc}-2 & 4 \ -5 & -5\end{array}ight] \cdot\left[\begin{array}{l}4 \ 5\end{array}ight] $$

UpStudy AI · Accepted Answer

We have
$$
\begin{pmatrix}
-2 & 4 \
-5 & -5
\end{pmatrix}
\begin{pmatrix}
4 \
5
\end{pmatrix}.
$$

1. Multiply the first row by the vector:
   $$
   (-2) \times 4 + 4 \times 5 = -8 + 20 = 12.
   $$

2. Multiply the second row by the vector:
   $$
   (-5) \times 4 + (-5) \times 5 = -20 - 25 = -45.
   $$

Thus, the resulting vector is
$$
\begin{pmatrix}
12 \
-45
\end{pmatrix}.
$$
The result of the matrix multiplication is: $$ \begin{pmatrix} 12 \ -45 \end{pmatrix} $$

4) \( \left[\begin{array}{cc}-2 & 4 \\ -5 & -5\end{array}\right] \cdot\left[\begin{array}{l}4 \\ 5\end{array}\right] \)

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