Jacobian matrix and determinant

A Jacobian Matrix is a type of matrix (a collection of numbers arranged in rows and columns) that helps you figure out how much a function changes when you tweak its inputs. A determinant is a number you can calculate from the values of a matrix. It describes how much something changes when its inputs are changed. To calculate the determinant of a Jacobian matrix, you have to plug in the values of all the numbers in the matrix and then use a formula to calculate the answer. The answer gives you an idea of how much the output of the function will change if you adjust the inputs.