Two matrices are row equivalent if they have the same number of rows.
Regarding your definition, it is not entirely correct
Regarding your definition, it is not entirely correct. Two matrices are considered row equivalent if one can be obtained from the other through a sequence of elementary row operations.
Elementary row operations include:
1. Swapping two rows
2. Multiplying a row by a non-zero scalar
3. Adding a multiple of one row to another row
To determine if two matrices are row equivalent, you need to perform these elementary row operations on one matrix to transform it into the other matrix. The order of operations is important, and the goal is to transform the first matrix into the second matrix.
By performing the same sequence of elementary row operations on both matrices, you can determine if they are row equivalent. If you can successfully transform one matrix into the other, they are row equivalent. Otherwise, if it is not possible to make them identical through these operations, they are not row equivalent.
Row equivalence is an important concept in linear algebra and plays a significant role in solving systems of linear equations, computing matrix inverses, and determining the rank of a matrix.
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