m427j.homework.6.solutions.pdf - M427J Differential Equations 1 Homework Systems of Linear Equations and Matrix Inverses For the following problems

# m427j.homework.6.solutions.pdf - M427J Differential...

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M427J - Differential Equations Homework 1Systems of Linear Equations and Matrix InversesFor the following problems, solve the given system by writing it as an augmented matrix andreducing the system (i.e., using Gauss-Jordan elimination). Then solve the system by finding thematrix inverseA-1and multiplyingA-1b1.3.x+ 4y+ 3z= 12x+ 8y+ 11z= 7x+ 6y+ 7z= 3 1 4 3 1 2 8 11 7 1 6 7 3 R 2 - 2 R 1 R 3 - R 1 1 4 3 1 0 0 5 5 0 2 4 2 R 2 R 3 1 4 3 1 0 2 4 2 0 0 5 5 1 2 R 2 1 5 R 3 1 4 3 1 0 1 2 1 0 0 1 1 R 1 - 4 R 2 1 0 - 5 - 3 0 1 2 1 0 0 1 1 R 1 + 5 R 3 R 2 - 2 R 3 1 0 0 2 0 1 0 - 1 0 0 1 1
M427J - Differential Equations Homework introducing fractions into the inverse as long as possible. 1 4 3 1 0 0 2 8 11 0 1 0 1 6 7 0 0 1 R 2 - 2 R 1 R 3 - R 1 1 4 3 1 0 0 0 0 5 - 2 1 0 0 2 4 - 1 0 1 R 2 R