4. \( \left[\begin{array}{ccc}1 & 2 & 2 \\ -1 & 1 & 3\end{array}\right] \cdot\left[\begin{array}{c}2 \\ -1\end{array}\right] \)

It seems there was an issue with the input format. Let's try to calculate the matrix multiplication manually. To calculate the matrix multiplication, we need to follow the rules of matrix multiplication. The result of multiplying two matrices is a new matrix where each element is the dot product of the corresponding row of the first matrix and the corresponding column of the second matrix. Given matrices: \[ A = \begin{bmatrix} 1 & 2 & 2 \\ -1 & 1 & 3 \end{bmatrix} \] \[ B = \begin{bmatrix} 2 \\ -1 \end{bmatrix} \] Let's calculate the result of the matrix multiplication step by step: 1. Multiply the first row of matrix A by the first column of matrix B: \[ (1 \times 2) + (2 \times -1) + (2 \times -1) = 2 - 2 - 2 = -2 \] 2. Multiply the first row of matrix A by the second column of matrix B: \[ (1 \times -1) + (2 \times 1) + (2 \times -1) = -1 + 2 - 2 = -1 \] 3. Multiply the second row of matrix A by the first column of matrix B: \[ (-1 \times 2) + (1 \times -1) + (3 \times -1) = -2 - 1 - 3 = -6 \] 4. Multiply the second row of matrix A by the second column of matrix B: \[ (-1 \times -1) + (1 \times 1) + (3 \times -1) = 1 + 1 - 3 = -1 \] Therefore, the result of the matrix multiplication is: \[ \begin{bmatrix} -2 & -1 \\ -6 & -1 \end{bmatrix} \]