3. Let A . Show that the system of linear equations Ax = b has a solution for all b if and only if the system of linear equations has no nonzero solutions.

7. (12 points) Let T: be a linear operator. Show that if T preserves the Euclidqdean distance between any two points, that is, ||T(u) - T(ข)||= ||u- ull for any u, u , then the matrix representation of T relative to the standard basis is an orthogonal matrix.