Part 5: Revisiting Systems of Linear Equations

Delving deeper into row operations

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What are Row Operations?

Photo by Glenn Carstens-Peters on Unsplash
  • Multiplying a row by a constant: Let’s say we have the numbers 2, 4, and 6 in the first row of a matrix. We can take all of those numbers and scale it by any factor we want (it can even be negative). For example, we could multiply each of the numbers in that first row by 2, resulting in our new row consisting of 4, 8, and 12.
  • Swapping Rows: This is exactly what it sounds like. Let’s say we have the numbers 1, 2, and 3 in row number 1, and the numbers 4, 5, and 6 in row number 2. We can swap these two rows such that row number 1 now consists of the numbers 4, 5, and 6 while row number 2 consists of the numbers 1, 2, and 3. This row operation is much less common compared to the other two. It is mostly used to get a row full of 0s to the bottom of the matrix.
  • Adding or Subtracting Rows: Let’s use the same initial example from the “swapping rows” bullet point. Row number 1 consists of numbers 1, 2, and 3, while row number 2 consists of the numbers 4, 5, and 6. We can actually change row 2 by adding (or subtracting) row 1 to itself! Let’s take the addition example. If we add row 1 to row 2, row 2 will now consist of the numbers 1 + 4, 2 + 5, and 3 + 6, or 5, 7, and 9.

The Mechanics

General Thinking

Concluding Thoughts

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