For the equations $x + 2 y + 3 z = 1, 2 x + y + 3 z = 2$ and $5 x + 5 y + 9 z = 4$

There is only one solution

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There exists infinitely many solution

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There is no solution

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None of the above

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Solution

The correct option is B There is only one solution
Given equations are $x + 2 y + 3 z = 1, 2 x + y + 3 z = 2$ and $5 x + 5 y + 9 z = 4$
The determinant of the coefficient matrix of given system of equation is $∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & 1 & 3 5 & 5 & 9 \end{matrix} ∣ ∣ ∣ ∣ = 1 (9 - 15) - 2 (18 - 15) + 3 (10 - 5) = 3 \neq 0$
Hence, the system of given equation has unique solution.

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Similar questions

x + 2 y + 3 z = 1, 2 x + y + 3 z = 2, 5 x + 5 y + 9 z = 4

x + 2 y + 3 z = 1

2 x + y + 3 z = 2

5 x + 5 y + 9 z = 4

x + y + z = 1, 2 x + 2 y + 3 z = 6, x + 4 y + 9 z = 3

k \in R,

3 x - y + 4 z = 3,

x + 2 y - 3 z = - 2,

6 x + 5 y + k z = - 3,

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