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Section 7.3 : Augmented Matrices

1. For the following augmented matrix perform the indicated elementary row operations. \[\left[ {\begin{array}{rrr|r}9&0&7&4\\{ - 3}&2&{ - 1}&{ - 7}\\2&4&1&2\end{array}} \right]\]
   1. \( - 4{R_{\,2}}\)
   2. \({R_{\,3}} \leftrightarrow {R_{\,1}}\)
   3. \({R_{\,1}} - 10{R_{\,3}} \to {R_{\,1}}\)
2. For the following augmented matrix perform the indicated elementary row operations. \[\left[ {\begin{array}{rrr|r}9&3&{11}&6\\{ - 2}&7&4&{ - 3}\\1&{ - 1}&1&{ - 1}\end{array}} \right]\]
   1. \(5{R_{\,1}}\)
   2. \({R_{\,2}} \leftrightarrow {R_{\,3}}\)
   3. \({R_{\,3}} - 2{R_{\,2}} \to {R_{\,3}}\)
3. For the following augmented matrix perform the indicated elementary row operations. \[\left[ {\begin{array}{rrr|r}4&{12}&{ - 8}&0\\{ - 9}&{ - 2}&1&3\\1&5&{ - 1}&{ - 10}\end{array}} \right]\]
   1. \(\frac{1}{3}{R_{\,3}}\)
   2. \({R_{\,1}} \leftrightarrow {R_{\,2}}\)
   3. \({R_{\,2}} + \frac{5}{2}{R_{\,1}} \to {R_{\,2}}\)
4. For the following augmented matrix perform the indicated elementary row operations. \[\left[ {\begin{array}{rrr|r}1&5&{ - 6}&{ - 2}\\{ - 3}&{ - 15}&{ - 18}&3\\4&{ - 2}&7&1\end{array}} \right]\]
   1. \( - 7{R_{\,3}}\)
   2. \({R_{\,1}} \leftrightarrow {R_{\,3}}\)
   3. \({R_{\,2}} + 3{R_{\,1}} \to {R_{\,2}}\)

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