| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2006 |
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| Session | November |
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| Topic | 3x3 Matrices |
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5 Show that if \(a \neq 3\) then the system of equations
$$\begin{aligned}
& 2 x + 3 y + 4 z = - 5
& 4 x + 5 y - z = 5 a + 15
& 6 x + 8 y + a z = b - 2 a + 21
\end{aligned}$$
has a unique solution.
Given that \(a = 3\), find the value of \(b\) for which the equations are consistent.