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Update main.tex
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VSP-0040/main.tex

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@@ -110,7 +110,7 @@ \subsection*{Row Space of a Matrix}
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$$\vec{w}=b_1\vec{r}_1+\ldots +\frac{b_i}{k}(k\vec{r}_i)+\ldots +b_m\vec{r}_m$$
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So $\vec{w}$ is in $\mbox{span}(\vec{r}_1,\ldots ,k\vec{r}_i,\ldots ,\vec{r}_m)$.
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We leave it to the reader to verify that adding a multiple of one row of $A$ to another does not change the row space. (See Practice Problem \ref{prob:proofofrowBrowA}.)
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We leave it to the reader to verify that adding a multiple of one row of $A$ to another does not change the row space. %(See Practice Problem \ref{prob:proofofrowBrowA}.)
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% Now suppose that $B$ was obtained from $A$ by adding $k$ times row $j$ to row $i$. We need to show that
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% $$\mbox{span}(\vec{r}_1,\ldots ,\vec{r}_i+k\vec{r}_j,\ldots ,\vec{r}_m)=\mbox{span}(\vec{r}_1,\ldots ,\vec{r}_i,\ldots ,\vec{r}_m)$$
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