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Subject:  Linear Algebra

Solve 2x + y = 5, x + 3y = 10

Solve a 2×2 linear system with Gauss-Jordan elimination.

Answer x1 = 1, x2 = 3

Solution

  1. System A is 2×2, b has 2 entries.
  2. Matrix A [[2, 1], [1, 3]]
  3. Vector b (5, 10)
  4. Augmented [A | b] [[2, 1, 5], [1, 3, 10]]
  5. Row operations R1 → (1/2)·R1; R2 → R2 − (1)·R1; R2 → (1/2.5)·R2; R1 → R1 − (0.5)·R2
  6. RREF of [A | b] [[1, 0, 1], [0, 1, 3]]
  7. Conclusion Unique solution — pivot in every variable column.
  8. Solution x1 = 1, x2 = 3

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