A single elimination step is shown on a 4x4 augmented matrix: the pivot entry 1 and the entry 2 below it are highlighted, and the row operation R2 ← R2 − 2R1 is carried out term by term across all four columns, including the right-hand side. The new row [0 4 4 | 8] replaces row 2 while the rest of the matrix stays visible, illustrating that such operations preserve the solution set. Intended for first-year economics or algebra students meeting matrix elimination for the first time.
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Create a calm mathematical teaching video explaining ONE step of Gaussian elimination. Learning objective: Understand why and how we eliminate an entry below a pivot, while preserving the solution set. Start with this augmented matrix: [1 1 0 | 3] [2 6 4 | 14] [0 8 3 | 11] [4 8 14 | 30] Keep the matrix visible throughout. 1. Highlight the pivot 1 in row 1 and the entry 2 directly below it. 2. Explain that our goal is to turn this 2 into zero. 3. Display R₂ ← R₂ − 2R₁. 4. Show each calculation in the second row: 2 − 2×1 = 0 6 − 2×1 = 4 4 − 2×0 = 4 14 − 2×3 = 8 5. Replace only row 2 with [0 4 4 | 8]. 6. Explain that the operation applies to the entire row, including the right-hand side, and preserves the solution set. Use large, readable mathematical notation, minimal text and consistent highlighting. Synchronize narration with each visual change. Pause briefly after important steps. No stock images, characters, music or unrelated theory. Do not solve the rest of the system. Audience: First-year university students in economics, with basic algebra knowledge but little experience with matrices.