Write an implicit equation for the 2d line through points

Question

1. Write an implicit equation for the 2D line through points (x₀, y₀) and (x₁, y₁) using a 2D determinant.

2. Show that if the columns of a matrix are orthonormal, then so are the rows.

3. Prove the properties of matrix determinants stated in Equations (5.5)-(5.7).

4. Show that the eigenvalues of a diagonal matrix are its diagonal elements