Questions: What is the value of determine ES?

Solution Steps

The question seems to be incomplete or unclear. However, if we assume that the task is to determine the value of a mathematical expression or a determinant, we can outline a general approach for finding the determinant of a matrix, which is a common mathematical task.

1. Identify the Matrix: Determine the matrix for which the determinant needs to be calculated.
2. Use a Mathematical Library: Utilize a Python library such as NumPy to compute the determinant efficiently.

The matrix given is

\[ \mathbf{A} = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

To find the determinant of the matrix \(\mathbf{A}\), we use the formula for a \(2 \times 2\) matrix:

\[ \text{det}(\mathbf{A}) = ad - bc \]

where \(a = 1\), \(b = 2\), \(c = 3\), and \(d = 4\). Thus, we have:

\[ \text{det}(\mathbf{A}) = (1)(4) - (2)(3) = 4 - 6 = -2 \]

The calculated determinant is

\[ \text{det}(\mathbf{A}) = -2.0000 \]

Final Answer