7 Three planes have equations
$$\begin{aligned}
( 4 k + 1 ) x - 3 y + ( k - 5 ) z & = 3
( k - 1 ) x + ( 3 - k ) y + 2 z & = 1
7 x - 3 y + 4 z & = 2
\end{aligned}$$
7
- The planes do not meet at a unique point.
Show that \(k = 4.5\) is one possible value of \(k\), and find the other possible value of \(k\).
| 7 | | For each value of \(k\) found in part (a), identify the configuration of the given planes. | | In each case fully justify your answer, stating whether or not the equations of the planes form a consistent system. | | [4 marks] \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) |
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