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- Explain the steps for solving a system of equations using Cramer’s rule.Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.A small business orders 3 different products from adistributor. Product X costs $2, product B\Y costs $3, and product Zcosts $5. The total cost of the order is $200 and the order is for a totalof 60 products. Set up and solve a system of equations for thissituation.a) What is the number of products X and Y if the number of Zproducts is 15?b) What is the most number of Z products in the order?
- A scientist solves a nonhomogeneous system of ten linear equations in twelve unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new nonhomogeneous system will have a solution? Discuss.Find general solutions of the systems in Problem Attached.Suppose a nonhomogeneous system of nine linear equations in ten unknowns has a solution for all possible constants on the right sides of the equations. Is it possible to find two nonzero solutions of the associated homogeneous system that are not multiples of each other? Discuss.
- Is it possible for a nonhomogeneous system of seven equations in six unknowns to have a unique solution for some right-hand side of constants? Is it possible for such a system to have a unique solution for every right-hand side? Explain.Solve the given system of equations using Gauss-Jordan Reduction method. 2.1) Gauss-Jordan Reduction MethodA homogeneous system of twelve linear equations in eight unknowns has two fixed solutions that are not multiples of each other, and all other solutions are linear combinations of these two solutions. Can the set of all solutions be described with fewer than twelve homogeneous linear equations? If so, how many? Discuss.
- Solve the given linear system using: II. Crammers RuleThe metal plate has constant temperature shown on its boundaries. Find equilibrium temperature at each of indicated interior point by setting up system of linear equation and obtain a solution by applying either the Gauss elimination or Gauss Jordan elimination method.Is is possible that all solutions of a homogeneous system of ten linear equations in twelve variables are multiples of one fixed nonzero solution? Discuss.