1. ## Determinants

How can I make something like determinants tangible? Are there real life examples where determinants are used?

2. What do you mean by "real life"?

3. Real life in the sense that the student will find motivating or likely to come across a particular example in physics, engineering, economics - really looking for a stimulating example. Thanks for the quick response.

4. You can think of the vector cross product as a determinant. The vector cross product shows up in electricity and magnetism, in Maxwell's Equations, as well as other places.

As a somewhat less spectacular example, you can think of Kramer's Rule for solving linear systems of equations. Kramer's Rule has more theoretical interest than practical, because computing determinants using, say, a Jacobian expansion is computationally intensive. For large problems, you'd probably try to diagonalize, or at least upper-triangularize (if that's a word) a matrix in order to compute its determinant as the product of the elements along the main diagonal.