question:find all real numbers λ such that the homogenous system

(λ

**I**n-A)

**x**=

**0** has a nontrivial solution

work:

. Then the answer key says that (λ

**I**n-A)

**x**=

**0 **has a nontrivial solution if and only if its determinant=0. So then to solve the problem the determinant is taken and the values for λ are used such that the determinant is 0. I'm sceptical about setting the determinant to 0

**because if a system has a determinant that is 0 then it means the system only has the trivial solution or infinetly many solutions** (emphasis added).