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### Section 7-3 : Augmented Matrices

1. For the following augmented matrix perform the indicated elementary row operations. $\left[ {\begin{array}{rrr|r}4&{ - 1}&3&5\\0&2&5&9\\{ - 6}&1&{ - 3}&{10}\end{array}} \right]$
1. $$8{R_{\,1}}$$
2. $${R_{\,2}} \leftrightarrow {R_{\,3}}$$
3. $${R_{\,2}} + 3{R_{\,1}} \to {R_{\,2}}$$
Solution
2. For the following augmented matrix perform the indicated elementary row operations. $\left[ {\begin{array}{rrr|r}1&{ - 6}&2&0\\2&{ - 8}&{10}&4\\3&{ - 4}&{ - 1}&2\end{array}} \right]$
1. $$\frac{1}{2}{R_{\,2}}$$
2. $${R_{\,1}} \leftrightarrow {R_{\,3}}$$
3. $${R_{\,1}} - 6{R_{\,3}} \to {R_{\,1}}$$
Solution
3. For the following augmented matrix perform the indicated elementary row operations. $\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&7&{ - 2}&3\end{array}} \right]$
1. $$- 9{R_{\,3}}$$
2. $${R_{\,1}} \leftrightarrow {R_{\,2}}$$
3. $${R_{\,3}} - {R_{\,1}} \to {R_{\,3}}$$
Solution

Note : Problems using augmented matrices to solve systems of equations are in the next section.