What makes 2 equations row equivalent?
If there is a series of elementary row operations that transforms one matrix into the other
Two equations are row equivalent if one equation can be obtained from the other by a sequence of elementary row operations. Elementary row operations include:
1) Swapping two rows
2) Multiplying a row by a non-zero constant
3) Adding a multiple of one row to another row
For example, consider the system of equations:
x + 2y = 5
2x + 3y = 8
We can use elementary row operations to transform this system into an equivalent system:
1) Adding -2 times the first row to the second row:
x + 2y = 5
0 + -1y = -2
This system is row equivalent to the original system because we can get from one to the other by applying elementary row operations. Specifically, we swapped the first and second rows (a type of elementary row operation), multiplied the first row by 1, and added -2 times the first row to the second row.
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