If `A=["-1 2 3"]andB=[(3),(-4),(0)]` find `|AB|`

Answer

To solve the problem, we need to find the product of matrices A and B, and then calculate the determinant of that product. Here are the steps:

### Step 1: Define the matrices A and B
Matrix A is given as:
\[ A = \begin{bmatrix} -1 & 2 & 3 \end{bmatrix} \]
Matrix B is given as:
\[ B = \begin{bmatrix} 3 \\ -4 \\ 0 \end{bmatrix} \]

### Step 2: Perform matrix multiplication
To find the product \( AB \), we multiply matrix A by matrix B. The multiplication is done as follows:

\[ AB = \begin{bmatrix} -1 & 2 & 3 \end{bmatrix} \begin{bmatrix} 3 \\ -4 \\ 0 \end{bmatrix} \]

Calculating the product:
\[ AB = (-1 \cdot 3) + (2 \cdot -4) + (3 \cdot 0) \]
\[ = -3 - 8 + 0 \]
\[ = -11 \]

### Step 3: Find the determinant of the product
Since the result of the multiplication \( AB \) is a scalar value (-11), the determinant of a scalar is simply the scalar itself. Therefore:
\[ |AB| = |-11| = 11 \]

### Final Answer
The determinant of the product \( |AB| \) is:
\[ \boxed{11} \]