If the points `(2,\ -3),\ (lambda,\ -1)` and `(0,\ 4)` are collinear, find the value of `lambdadot`

Explanation

To determine the value of \( \lambda \) such that the points \( (2, -3) \), \( (\lambda, -1) \), and \( (0, 4) \) are collinear, we can use the condition that the area of the triangle formed by these points is zero. This can be expressed using the determinant of a matrix formed by the coordinates of the points.

### Step-by-Step Solution:

1. **Set up the determinant for collinearity**:
The points are collinear if the following determinant is equal to zero:
\[
\begin{vmatrix}
...