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

2 x + 3 y + 2 z = 9

3 x + 2 y + 2 z = 9

x - y + 4 z = 8

A =

⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 & 5 3 & 2 & - 4 1 & 1 & - 2 \end{matrix} ⎤ ⎥ ⎦

A^{- 1}

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} ⎤ ⎥ ⎦, find A^{- 1} .

A^{- 1}

2 x - 3 y + 5 z = 11, 3 x + 2 y - 4 z = - 5, x + y - 2 z = - 3.

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

x - y + 2 z = 1

2 y - 3 z = 1

3 x - 2 y + 4 z = 2

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