First slide

System of linear equations

Question

The value of ‘a’ for which the equations $3 x - y + a z = 1, 2 x + y + z = 2, x + 2 y - a z = - 1$ fail to have unique solution

Moderate

A

$\frac{7}{2}$
B

$- \frac{7}{2}$
C

$\frac{2}{7}$
D

$- \frac{2}{7}$

Solution

the condition for a non-homogeneous system fails to have a unique solution is $|A| = 0$
$\Rightarrow |A| = |\begin{array}{l} 3 - 1 a \\ 2 1 1 \\ 1 2 - a \end{array}| = 0 \Rightarrow 3 [- a - 2] + 1 [- 2 a - 1] + a [4 - 1] = 0$
$\begin{array}{l} \Rightarrow - 3 a - 6 - 2 a - 1 + 3 a = 0 \\ \Rightarrow - 7 = 2 a \Rightarrow a = - 7 / 2 \end{array}$

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