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(a)\quad Rowreduce each matrix and determine that the reduced rowechelon forms of $B$ and $C$ are identical. From this argue that $B$ and $C$ are rowequivalent.<br /><br />
(b)\quad In the proof of <acroref type="theorem" acro="RREFU" />, we begin by arguing that entries of rowequivalent 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
+<li>Rowreduce each matrix and determine that the reduced rowechelon forms of $B$ and $C$ are identical. From this argue that $B$ and $C$ are rowequivalent.</li>
+<li>In the proof of <acroref type="theorem" acro="RREFU" />, we begin by arguing that entries of rowequivalent 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
For each $1\leq i\leq 3$ find the corresponding three scalars in this relationship. So your answer will be nine scalars, determined three at a time.
+For each $1\leq i\leq 3$ find the corresponding three scalars in this relationship. So your answer will be nine scalars, determined three at a time.</li>
<solution contributor="robertbeezer">(a)\quad Let $R$ be the common reduced rowechelon form of $B$ and $C$. A sequence of row operations converts $B$ to $R$ and a second sequence of row operations converts $C$ to $R$. If we <q>reverse</q> the second sequence's order, and reverse each individual row operation (see <acroref type="exercise" acro="RREF.T10" />) then we can begin with $B$, convert to $R$ with the first sequence, and then convert to $C$ with the reversed sequence. Satisfying <acroref type="definition" acro="REM" /> we can say $B$ and $C$ are rowequivalent matrices.<br /><br />
(b)\quad We will work this carefully for the first row of $B$ and just give the solution for the next two rows. For row 1 of $B$ take $i=1$ and we have
+<li>Let $R$ be the common reduced rowechelon form of $B$ and $C$. A sequence of row operations converts $B$ to $R$ and a second sequence of row operations converts $C$ to $R$. If we <q>reverse</q> the second sequence's order, and reverse each individual row operation (see <acroref type="exercise" acro="RREF.T10" />) then we can begin with $B$, convert to $R$ with the first sequence, and then convert to $C$ with the reversed sequence. Satisfying <acroref type="definition" acro="REM" /> we can say $B$ and $C$ are rowequivalent matrices.</li>
+<li>We will work this carefully for the first row of $B$ and just give the solution for the next two rows. For row 1 of $B$ take $i=1$ and we have