Question
4) \( \left[\begin{array}{cc}-2 & 4 \\ -5 & -5\end{array}\right] \cdot\left[\begin{array}{l}4 \\ 5\end{array}\right] \)
Ask by Elliott Chandler. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The result of the matrix multiplication is:
\[
\begin{pmatrix}
12 \\
-45
\end{pmatrix}
\]
Solution
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Mind Expander
To multiply the matrix \( \left[\begin{array}{cc}-2 & 4 \\ -5 & -5\end{array}\right] \) by the vector \( \left[\begin{array}{l}4 \\ 5\end{array}\right] \), we can follow the matrix multiplication rules. For the first row, we calculate: \(-2 \cdot 4 + 4 \cdot 5 = -8 + 20 = 12\). For the second row, we calculate: \(-5 \cdot 4 + (-5) \cdot 5 = -20 - 25 = -45\). Thus, the result of the multiplication is: \[ \left[\begin{array}{l}12 \\ -45\end{array}\right]. \]
