The following system of linear equations
$2 x + 3 y + 2 z = 9$
$3 x + 2 y + 2 z = 9$
$x - y + 4 z = 8$

does not have any solution

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has an unique solution

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has a solution (α, β, γ) satisfying α + β^{2} + γ^{3} = 12

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has infinitely many solutions

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Solution

The correct option is B has an unique solution
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 3 & 2 3 & 2 & 2 1 & - 1 & 4 \end{matrix} ∣ ∣ ∣ ∣ = - 20 \neq 0$
It has unique solution.

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Similar questions

x + y + 2 z = 4; 2 x + 2 y + 4 z = 8; 3 x + 3 y + 6 z = 10

2 x - 3 y + 5 z = 11

3 x + 2 y - 4 z = - 5

x + y - 2 z = - 3

A = [\begin{matrix} 2 & - 3 & 5 \\ 3 & 2 & - 4 \\ 1 & 1 & - 2 \end{matrix}]

Solve the following system of linear equations, using matrix method

$2 x + 3 y + 3 z = 5, x - 2 y + z = - 4, 3 x - y - 2 z = 3$

y + 2 z = 7

x - y = 3

2 x + 3 y + 4 z = 17

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