Use Gaussian elimination to find the complete solution to the system of given equations, or show that none exists. {(2x-4y+z=3),(x-3y+z=5),(3x-7y+2z=12):}

Alyce Wilkinson 2021-01-19 Answered
Use Gaussian elimination to find the complete solution to the system of given equations, or show that none exists.
{2x4y+z=3x3y+z=53x7y+2z=12
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Expert Answer

ottcomn
Answered 2021-01-20 Author has 97 answers
Step 1
Consider the system of equations,
{2x4y+z=3x3y+z=53x7y+2z=12
Step 2
The augmented matrix is constructed as below.
[2413131537212]
Use Gaussian elimination to find the complete solution to the system of given equations.
Apply the row operation R1R2
[1315241337212]
Apply the row operation R2R22R1 to the above matrix.
[1313021737212]
Aply the row operation R3R33R1 to the above matrix.
[131302170213]
Aply the row operation R212R2 to the above matrix.
[13150112720213]
Apply the row operation R2R32R2 to the above matrix.
[13150112720004]
Translate the last row back in to equation form as, 0x+0y+0z=4 which is false equation since it is impossible to find the solution to the given system of equations.
Thus, the system has no solution.
Therefore, the solution set of the system of equations is an empty set.
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