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Solving System of Linear Equations Using Inverse

If system of ...

Question

If system of equations ax + y + z = a, x + by + z = b and x + y + cz = c is inconsistent, then which of the following is correct?

a b c - a - b - c + 2 = 0

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a b c - a - b - c + 3 = 0

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a b c - a - b - c + 3 = 0, a = 1

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a b c - a - b - c + 2 = 0, a \neq 1, b \neq 1, c \neq 1

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Solution

The correct option is D $a b c - a - b - c + 2 = 0, a \neq 1, b \neq 1, c \neq 1$
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} a & 1 & 1 1 & b & 1 1 & 1 & c \end{matrix} ∣ ∣ ∣ ∣ = 0$ for inconsistent
abc - a-b-c +2=0
$a \neq 1, b \neq 1, c \neq 1$

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