Mathematics, 07.09.2019 04:20 sarah5707
Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (if not possible, enter impossible.) x + y = 4 y + z = 4 x + z = 4 ax + by + cz = 0
Answers: 3
![\left[\begin{array}{ccc}1&1&0\\0&4&1\\4a&b&c\end{array}\right]](/tpl/images/0225/0835/61a51.png)
![-4aR_{1}+R_{3}\rightarrow R_{3}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4&1\\0&(-4a+b)&c\end{array}\right]](/tpl/images/0225/0835/2c512.png)
![(4a-b)R_{2}+4R_{3} \rightarrow R_{3}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4&1\\0&0&(4a-b+c)\end{array}\right]](/tpl/images/0225/0835/585ed.png)
![(4a-b+c)R_{2}-R_{3} \rightarrow R_{2}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4(4a-b+c)&0\\0&0&(4a-b+c)\end{array}\right]](/tpl/images/0225/0835/b19f5.png)
![4(4a-b+c)R_{1}-R_{2} \rightarrow R_{1}\\\\{\left[\begin{array}{ccc}4(4a-b+c)&0&0\\0&4(4a-b+c)&0\\0&0&(4a-b+c)\end{array}\right]](/tpl/images/0225/0835/c7d46.png)
![\left[\begin{array}{ccc}16&-4&4\\16&-4&4\\4&-1&1\end{array}\right]](/tpl/images/0225/0835/d2a2d.png)
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Find values of a, b, and c (if possible) such that the system of linear equations has a unique solut...
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