Linear Algebra - Sytems of linear equations

Here are some linear algebraic questions :P These are the question and will send their solution at next article.

1.Which condition must be placed on a, b, and c so that the following system of equations has a solution?



2. Determine if the given system has a nonzero solution.



3. Determine the values of a so that the given system of linear equations has (i) no solution,(ii) more than one solution, (iii) unique solution.



4. Consider the system of linear equations. Suppose that the system has only the trivial solution when all bi are zero. Show that this system has a unique solution for every other choice of the constants bi.