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Question: m309 homework 1 1 as discussed in class it...

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M309 - Homework 1 1. As discussed in class, it is possible to solve two systems simultaneously as long as they have the same coefficient matrix. Solve the two systems 2x1 + 2x2+ x3-5and simultaneously by first forming a 3 x 5 augmented matrix, row reducing to STF, and then finally performing two separate back substitutions per system.

M309 Spring 2019 O, R.G. Lynch, Texas A&M Homework 1, Page 2 of 7 2. A system of linear equations is said to be homogeneous if the constants on the right-hand side -216r2 +x3 -15a0 6x1-18x2+ x3 + 1724 = 0 are all zero. The system is an example of a homogeneous system. Homogeneous systems always have at least one solu- tion, namely the tuple consisting of all zeros: (0,0,...,0). This solution of all zeros is called the trivial solution and any other solution is called nontrivial. It turns out that any underdeter- mined homogeneous system also has at least one nontrivial solution since there will necessarily be free variables that can be taken to be anything we want. Thus, we can conclude that underdetermined homogeneous systems always have infinitely many solutions! With this knowledge in hand, how many solutions do you expect that the system above has? To confirm your answer, write the augmented matrix of the homogeneous system above, reduce it to reduced row echelon form (RREF), and then solve. Circle your final answer.

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