title: Difference between a linear problem and a non-linear problem? Essence of Dot-Product and Kernel trick
body: <p>The kernel trick maps a non-linear problem into a linear problem. </p>
  
  <p>My questions are:<br>
  1. What is the main difference between a linear and a non-linear problem? What is the intuition behind the difference of these two classes of problem? And How does kernel trick helps use the linear classifiers on a non-linear problem?<br>
  2. Why is the dot product so important in the two cases? </p>
  
  <p>Thanks.</p>