Find AB

Given:

\[ A = \begin{bmatrix} 4 & 3 \\ 1 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} -4 \\ 3 \end{bmatrix} \]

Step 1: Check Order

\[ A \text{ is } 2 \times 2, \quad B \text{ is } 2 \times 1 \]

\[ AB \text{ exists and will be of order } 2 \times 1 \]

Step 2: Multiply A and B

\[ AB = \begin{bmatrix} 4 & 3 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} -4 \\ 3 \end{bmatrix} = \begin{bmatrix} 4(-4) + 3(3) \\ 1(-4) + 2(3) \end{bmatrix} \]

\[ AB = \begin{bmatrix} -16 + 9 \\ -4 + 6 \end{bmatrix} = \begin{bmatrix} -7 \\ 2 \end{bmatrix} \]

Final Answer:

\[ AB = \begin{bmatrix} -7 \\ 2 \end{bmatrix} \]