2. La Ley de Hooke establece que, dentro de ciertos límites, hay una relación lineal entre la fuerza mathrm(F) ejercida por un resorte y la longitud l de éste. Es decir, que existen números reales alpha y beta tales que F=a l+beta . Usar los siguientes datos para estimar las constantes alpha y beta : Longitud (mathrm(cm)) & Fuerza (mathrm(N)) 8.89 & 4.5 10.2 & 9.8 11.4 & 12.5 12.7 & 19.1

## Step 1: Understand the Problem### We are given a linear relationship between force and length of a spring, expressed as . Our task is to estimate the constants and using the provided data points.## Step 2: Set Up the System of Equations### Using the given data points, we can set up a system of equations. Each pair of (length, force) gives us an equation:- For , : - For , : - For , : - For , : ## Step 3: Solve the System of Equations### To find the best estimates for and , we can use the method of least squares, which minimizes the sum of the squares of the residuals (the differences between the observed and predicted values).### The normal equations for least squares in this context are: where is the number of data points.### Calculating these sums from the data:- - - - ### Substituting these into the normal equations: ## Step 4: Solve the Linear System### Solving these equations simultaneously (using methods such as substitution or matrix operations), we find:- -