Solve the system of equations using matrices.Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. {x+y−z=−22x−y+z=5−x+2y+2z=1

Question

Solve the system of equations using matrices.Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.  {x+y−z=−22x−y+z=5−x+2y+2z=1

Dora · Accepted Answer

Step 1  Given:  The system of linear equations are,  x+y−z=−2  2x−y+z=5  −x+2y+2z=1  For applying Gauss-Jordan elimination method, the above system of equations can be represented in matrix form as,  [11−1−22−115−1221]  Step 2  The above matrix can be converted into row echelon form as,  [11−1−20−339−1221](By applying: R2→R2−2R1)  [11−1−20−339031−1](By applying: R3→R3+R1)  [11−1−201−1−3031−1](By applying: R2→−13R2)  [11−1−201−1−30048](By applying: R3→R3−3R2)  Step 3  [11−1−201−1−30012]  (By applying: R3→14R3)  [11−1−2010−10012]  (By applying: R2→R2+R3)  [1100010−10012]  (By applying: R1→R1+R3)  Step 4  [1001010−10012]  (By applying: R1→R1−R2)  Hence, the solutions of the given system of equations are x=1 , y=-1 and z=2

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Solve the system of equations using matrices.Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. begin{cases}x+y-z=-22x-y+z=5-x+2y+2z=1end{cases}

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