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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.