Mathematics, 10.10.2019 01:00 damianb25
The sum of the length, width, and height of a rectangular box is 16 cm; the width is twice the height; and twice the length exceeds the sum of the width and height by 5. find the length, width, and height of the box using matrices. a. length = 10 cm, width = 4 cm, height = 2 cm b. length = 7 cm, width = 6 cm, height = 3 cm c. length = 7 cm, width = 3 cm, height = 6 cm d. length = 10 cm, width = 2 cm, height = 4 cm
Answers: 3
![\left[\begin{array}{ccc}1&1&1\\0&1&-2\\2&-1&-1\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right] = \left[\begin{array}{c}16&0&5\end{array}\right] \ \ -2R_1+R_3 \rightarrow R_3 \\ \left[\begin{array}{ccc}1&1&1\\0&1&-2\\0&-3&-3\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right]=\left[\begin{array}{c}16&0&-27\end{array}\right] \ \ \frac{1}{3} R_3+R_1 \rightarrow R_1](/tpl/images/0305/2743/8fc80.png)
![\left[\begin{array}{ccc}1&0&0\\0&1&-2\\0&-3&-3\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right]=\left[\begin{array}{c}7&0&-27\end{array}\right] \ \ 3 R_2+R_3 \rightarrow R_3 \\ \left[\begin{array}{ccc}1&0&0\\0&1&-2\\0&0&-9\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right]=\left[\begin{array}{c}7&0&-27\end{array}\right] \ \ - \frac{1}{9} R_3 \rightarrow R_3](/tpl/images/0305/2743/168a7.png)
![\left[\begin{array}{ccc}1&0&0\\0&1&-2\\0&0&1\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right]=\left[\begin{array}{c}7&0&3\end{array}\right] \ \ 2R_3+R_2 \rightarrow R_2 \\ \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{c}l&w&h\end{array}\right]=\left[\begin{array}{c}7&6&3\end{array}\right]](/tpl/images/0305/2743/ef2cb.png)
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