Practice Systems
A system of equations is a set of two or more equations that are related by the fact that they are both sets of variables with one or more common variables. It is recitation again. You have studied matrices and their various applications. One of them is to solving systems of linear equations. Here for you is a system of three linear equations: 2x + cz = 4, x – y + 2z = n, and x – 2y + 2z = -12 Please find the value of c or all values of c for which, first of all, there is a unique solution to this system, second of all, for which the corresponding homogeneous system has a unique solution. Thus, the corresponding homogeneous system is the system where you replace these constants on the right by 0. It is a very similar-looking system. The left-hand sides are all the same, but the right-hand sides are replaced with 0. What you need is to find the value of c for which this system has a unique solution, the value of c for which the corresponding homogeneous system has a unique solution, and also the values of c for which the corresponding homogeneous system has infinitely many solutions. Note that this system of equations is not being solved here, although you are welcome to solve it if you like. Note, however, that the value of c might affect your ability to do so. Think over. Consider the system 2x + CZ=4 X- y +2z = pi x-2y+2 z=-12 Find c for which a) there is a unique solution b) the corresponding homogeneous system has a unique solution c) the homogeneous system has infinitely many solution
