First slide

System of linear equations

Question

The values of a for which the system of equations $x + y + z = 1, x + 2 y + 4 z = α, x + 4 y + 10 z = α^{2}$ is consistent is given by

Easy

A

1,-2
B

-1,2
C

1,2
D

None of these

Solution

$x + y + z = 1___(1)$
$x + 2 y + 4 z = α_(2)$
$x + 4 y + 10 z = α^{2}____(3)$
Sub 1st eqn from 2 & 3 we have
$\begin{array}{l} y + 3 z = α - 1 ∣ \\ 3 y + 9 z = α^{2} - 1 \\ \Rightarrow α^{2} - 1 = 3 (α - 1) = 1 \Rightarrow α = 1 o r α = 2 \end{array}$

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