3) \( \left[\begin{array}{ll}-2 & 5\end{array}\right] \cdot\left[\begin{array}{cc}-3 & -1 \\ 1 & 1\end{array}\right] \)

Matrices by following steps: - step0: Solution: \(\left[\begin{array}{ll}{-2}&{5}\end{array}\right]\times \left[\begin{array}{ll}{-3}&{-1}\\{1}&{1}\end{array}\right]\) - step1: Multiply the terms: \(\left[\begin{array}{ll}{-2\left(-3\right)+5\times 1}&{-2\left(-1\right)+5\times 1}\end{array}\right]\) - step2: Evaluate: \(\left[\begin{array}{ll}{11}&{7}\end{array}\right]\) To calculate the product of the matrices \( \left[\begin{array}{ll}-2 & 5\end{array}\right] \) and \( \left[\begin{array}{cc}-3 & -1 \\ 1 & 1\end{array}\right] \), we perform the following steps: 1. **Matrix Dimensions**: The first matrix is a \( 1 \times 2 \) matrix, and the second matrix is a \( 2 \times 2 \) matrix. The product will be a \( 1 \times 2 \) matrix. 2. **Matrix Multiplication**: The multiplication is done by taking the dot product of the rows of the first matrix with the columns of the second matrix. - For the first element: \[ (-2) \cdot (-3) + (5) \cdot (1) = 6 + 5 = 11 \] - For the second element: \[ (-2) \cdot (-1) + (5) \cdot (1) = 2 + 5 = 7 \] 3. **Result**: Therefore, the resulting matrix is: \[ \left[\begin{array}{ll} 11 & 7 \end{array}\right] \] Thus, the final answer is: \[ \left[\begin{array}{ll} 11 & 7 \end{array}\right] \]