Consider the system of equations a1x-b1y-c1z- 0 a2x-b2y-c2z- 0 a3x-b3y-c3z- 0 if - a1 b1 c1 a2 b2 c3 a3 b3 c3 - 0- then the system has

The correct option is A more than two solutions D= | a_1 amp;b_1 nbsp; amp;c_1 nbsp; nbsp;a_2 amp;b_2 nbsp; amp;c_3 nbsp; nbsp ...

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nCr Definitions and Properties

Consider the ...

Question

Consider the system of equations
$a_{1} x + b_{1} y + c_{1} z = 0$
$a_{2} x + b_{2} y + c_{2} z = 0$
$a_{3} x + b_{3} y + c_{3} z = 0$
$i f ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{3} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0,$ then the system has

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|\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}|

A = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & a_{3} \end{matrix} ∣ ∣ ∣ ∣ \neq 0,

a_{1} x + b_{1} y + c_{1} z = 0, a_{2} x + b_{2} y + c_{2} z = 0

a_{3} x + b_{3} y + c_{3} z = 0

A = ⎡ ⎢ ⎣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ⎤ ⎥ ⎦

| A | \neq 0

a_{1} x + b_{1} y + c_{1} z = 0, a_{2} x + b_{2} y + c_{2} z = 0

a_{3} x + b_{3} y + c_{3} z = 0

a_{1} x + b_{1} y + c_{1} z = 0 . . . (1),

a_{2} x + b_{2} y + c_{2} z = 0 . . . (2),

a_{3} x + b_{3} y + c_{3} z = 0 . . . (3)

b c + q r = c a + r p = a b + p q = - 1

∣ ∣ ∣ ∣ \begin{matrix} a p & a & p b q & b & q c r & c & r \end{matrix} ∣ ∣ ∣ ∣ = 0 (a b c, p q r \neq 0)

a_{1} x + b_{1} y + c_{1} = 0, a_{2} x + b_{2} y + c_{2} = 0, a_{3} x + b_{3} y + c_{3} = 0

∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣ = 0

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