If x x-y x-y-z 2x 3x-2y 4x-3y-2z 3x 6x-3y 10x-6y-3z -64- then the real value of x is -

=x 1 nbsp; amp; x+y nbsp; amp; x+y+z 2 amp; 3x+2y nbsp; amp; 4x+3y+2z 3 amp; 6x+3y amp; 10x+6y+3z Using C _ 3 → ...

197

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Properties of Determinants

If x x+y ...

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If $∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 3 x + 2 y & 4 x + 3 y + 2 z 3 x & 6 x = 3 y & 10 x + 6 y + 3 z \end{matrix} ∣ ∣ ∣ ∣ = 64$ , then the real value of $x$ is .........

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∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 3 x + 2 y & 4 x + 3 y + 2 z 3 x & 6 x + 3 y & 10 x + 6 y + 3 z \end{matrix} ∣ ∣ ∣ ∣

64

⎡ ⎢ ⎣ \begin{matrix} x & x + y & x + y + z 2 x & 3 x + 2 y & 4 x + 3 y + 2 z 3 x & 6 x + 3 y & 10 x + 6 y + 3 z \end{matrix} ⎤ ⎥ ⎦ = 64

x =

x, y, z \in R

△ = ∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 5 x + 2 y & 7 x + 5 y + 2 z 3 x & 7 x + 3 y & 9 x + 7 y + 3 z \end{matrix} ∣ ∣ ∣ ∣ = - 16

x

x, y, z \in R, Δ = ∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 5 x + 2 y & 7 x + 5 y + 2 z 3 x & 7 x + 3 y & 9 x + 7 y + 3 z \end{matrix} ∣ ∣ ∣ ∣ = - 16

x

x, y, z \in R

Δ = ∣ ∣ ∣ ∣ \begin{matrix} x & x + y & x + y + z 2 x & 5 x + 2 y & 7 x + 5 y + 2 z 3 x & 7 x + 3 y & 9 x + 7 y + 3 z \end{matrix} ∣ ∣ ∣ ∣ = - 16

x

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