2. Homogeneous systems of equations. A homogeneous system of equations is a system of the form a a a. $1 0 11 12 111 $2 0 aml 37712 ' ' ' amn zen 0 (a) Prove that a homogeneous system always has the trivial solution as one solution. The trivial solution is the solution ($1,332, . .. , at\") = (0, 0, . . . , 0). (b) Prove that a homogeneous system has a nontrivial solution if and only if the system has at least one free variable. (c) Given a homogeneous system of m. linear equations in n unknowns if n > m (i.e. there are more unknowns than equations) there will be innitely many solutions to the system. ((1) Prove / Disprove/ Salvage. The homogeneous system of equations am+by=0 cm+dy=0 has only one solution if and only if a 0 5A 0 and b d 79 0