(Solution) - Consider the two 3 4 matrices below 1 Row reduce each -(2025 Original AI-Free Solution)

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Consider the two 3 × 4 matrices below

1. Row-reduce each matrix and determine that the reduced row-echelon forms of B and C are identical.
From this argue that B and C are row-equivalent.
2. In the proof of Theorem RREFU, we begin by arguing that entries of row-equivalent matrices are related by way of certain scalars and sums. In this example, we would write that entries of B from row i that are in column j are linearly related to the entries of C in column j from all three rows
[B]ij = ?i1 [C]1j + ?i2 [C]2j + ?i3 [C]3j
For each 1 ? i ? 3 find the corresponding three scalars in this relationship. So your answer will be nine scalars, determined three at a time.