Systems of Equations: A Practice Exercise with Multiple Cases

University
Massachusetts Institute of Technology
Course
Multivariable Calculus
Pages

1

Academic year

2022
Author

Sporkz
Views

33

p {margin: 0; padding: 0;} .ft00{font-size:20px;font-family:Arial;color:#000000;} .ft01{font-size:18px;font-family:Arial;color:#000000;} .ft02{font-size:18px;font-family:ArialMT;color:#000000;} .ft03{font-size:18px;line-height:22px;font-family:Arial;color:#000000;} .ft04{font-size:18px;line-height:22px;font-family:ArialMT;color:#000000;} Practice Systems A system of equations is a set of two or more equations that are related by the fact thatthey 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 themis to solving systems of linear equations. Here for you is a system of three linear equations: 2x + cz = 4, x – y + 2z = π, 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 solutionto this system, second of all, for which the corresponding homogeneous system has aunique solution. Thus, the corresponding homogeneous system is the system where you replace theseconstants 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. Whatyou need is to find the value of c for which this system has a unique solution, the value of cfor which the corresponding homogeneous system has a unique solution, and also thevalues of c for which the corresponding homogeneous system has infinitely manysolutions. Note that this system of equations is not being solved here, although you are welcome tosolve it if you like. Note, however, that the value of c might affect your ability to do so. Think over.