Subjects linear algebra

Row Equivalence 7A7F77

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1. The problem is to determine which pairs of matrices are row equivalent. 2. Two matrices are row equivalent if one can be transformed into the other by a sequence of elementary row operations (row swaps, scaling rows by nonzero constants, and adding multiples of one row to another). 3. We examine the given matrices in pairs to check if one can be obtained from the other by these operations. 4. For example, consider the first and second matrices: $$\begin{bmatrix}6 & 34 & 30 & 26 \\ 24 & 42 & 30 & 39 \\ 30 & 25 & 35 & 10\end{bmatrix}$$ and $$\begin{bmatrix}24 & 42 & 30 & 39 \\ 30 & 25 & 35 & 10 \\ 6 & 34 & 30 & 26\end{bmatrix}$$ 5. Notice the second matrix is obtained by swapping the first and third rows of the first matrix, which is an elementary row operation. 6. Therefore, these two matrices are row equivalent. 7. Similarly, check other pairs by comparing rows and possible row operations. Final answer: The first and second matrices are row equivalent because one can be obtained from the other by swapping rows.