Use Gaussian elimination to find the complete solution to the system of given equations, or show that none exists. {2x−4y+z=3x−3y+z=53x−7y+2z=12

Question

Use Gaussian elimination to find the complete solution to the system of given equations, or show that none exists.  {2x−4y+z=3x−3y+z=53x−7y+2z=12

ottcomn · Accepted Answer

Step 1  Consider the system of equations,  {2x−4y+z=3x−3y+z=53x−7y+2z=12  Step 2  The augmented matrix is constructed as below.  [2−4131−3153−7212]  Use Gaussian elimination to find the complete solution to the system of given equations.  Apply the row operation R1↔R2  [1−3152−4133−7212]  Apply the row operation R2→R2−2R1 to the above matrix.  [1−31302−1−73−7212]  Aply the row operation R3→R3−3R1 to the above matrix.  [1−31302−1−702−1−3]  Aply the row operation R2→12R2 to the above matrix.  [1−31501−12−7202−1−3]  Apply the row operation R2→R3−2R2 to the above matrix.  [1−31501−12−720004]  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.

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):}

Answered question

Answer & Explanation

New Questions in Algebra II