Final answer:
A linear decision boundary is a line that separates different classes based on values of input variables. It can be represented by a linear equation, but if we allow for nonlinearity, we can use nonlinear functions to define the boundary. Nonlinearity introduces curvature and captures more complex relationships between variables.
Step-by-step explanation:
In this question, we are discussing linear decision boundaries. A linear decision boundary is a line that separates different classes or categories in a classification problem. It separates the input space into two regions based on the values of the input variables. In a linear decision boundary, the relationship between the input variables can be represented by a linear equation of the form y = mx + b. However, this equation does not allow for nonlinearity. If we allow for nonlinearity, we can use nonlinear functions of the input variables such as x², x1x2, etc. to define the decision boundary. These nonlinear terms introduce curvature and allow us to capture more complex relationships between the input variables. Overall, a linear decision boundary without nonlinearity is a simple straight line, while allowing for nonlinearity can lead to more flexible and accurate classification models.