If - 1-7 x 2 -5 x-1 3 4 x 7 - - 2-x 2 7 x-1 3 -5 x 7 4 then - 1- 2-0 for

The correct option is D all real x Given, #160; Δ _1=7 amp;x #160; amp;2 5 amp;x+1 #160; amp;3 4 amp;x #160; am ...

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Byju's Answer

Standard XII

Mathematics

Cofactor

If Δ 1=7 x...

Question

If $Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 7 & x & 2 - 5 & x + 1 & 3 4 & x & 7 \end{matrix} ∣ ∣ ∣ ∣, Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x & 2 & 7 x + 1 & 3 & - 5 x & 7 & 4 \end{matrix} ∣ ∣ ∣ ∣$ then $Δ_{1} - Δ_{2} = 0$ for

x = 2

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all real

x

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x = 0

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none of these

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Solution

The correct option is D all real $x$
Given, $Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 7 & x & 2 - 5 & x + 1 & 3 4 & x & 7 \end{matrix} ∣ ∣ ∣ ∣$
$C_{1} \leftrightarrow C_{2}$
$Δ_{1} = - ∣ ∣ ∣ ∣ \begin{matrix} x & 7 & 2 x + 1 & - 5 & 3 x & 4 & 7 \end{matrix} ∣ ∣ ∣ ∣$
$C_{2} \leftrightarrow C_{3}$
$= ∣ ∣ ∣ ∣ \begin{matrix} x & 2 & 7 x + 1 & 3 & - 5 x & 7 & 4 \end{matrix} ∣ ∣ ∣ ∣$
$= Δ_{2}$
$\Rightarrow Δ_{1} = Δ_{2}$ for all real x

Suggest Corrections

Similar questions

Q. If

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 10 & 4 & 3 17 & 7 & 4 4 & - 5 & 7 \end{matrix} ∣ ∣ ∣ ∣, Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} 4 & x + 5 & 3 7 & x + 12 & 4 - 5 & x - 1 & 7 \end{matrix} ∣ ∣ ∣ ∣

such that

Δ_{1} + Δ_{2} = 0

then

Q. If

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} x & sin θ & cos θ - sin θ & - x & 1 cos θ & 1 & x \end{matrix} ∣ ∣ ∣ ∣

and

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x & sin 2 θ & cos 2 θ - sin 2 θ & - x & 1 cos 2 θ & 1 & x \end{matrix} ∣ ∣ ∣ ∣

x \neq 0

; then for all

θ \in (0, \frac{π}{2})

Q. If

∆_{1} = |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix}|, ∆_{2} = |\begin{matrix} 1 & b c & a \\ 1 & c a & b \\ 1 & a b & c \end{matrix}|, then

(a)

∆_{1} + ∆_{2} = 0

(b)

∆_{1} + 2 ∆_{2} = 0

(c)

∆_{1} = ∆_{2}

(d) none of these

Q. Let

Δ_{1} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & cos α & cos β cos α & 1 & cos γ cos β & cos γ & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

and

Δ_{2} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & cos α & cos β cos α & 0 & cos γ cos β & cos γ & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ_{1} = Δ_{2}

, find

{sin}^{2} α + {sin}^{2} β + {sin}^{2} γ

$Δ_{1}$ , $∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{2} & b^{2} & c^{2} \end{matrix} ∣ ∣ ∣ ∣$ , $Δ_{2}$ = $∣ ∣ ∣ ∣ \begin{matrix} 1 & b c & a 1 & c a & b 1 & a b & c \end{matrix} ∣ ∣ ∣ ∣$ then

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If Δ1=∣∣ ∣∣7x2−5x+134x7∣∣ ∣∣,Δ2=∣∣ ∣∣x27x+13−5x74∣∣ ∣∣ then Δ1−Δ2=0 for

The correct option is D all real xGiven, Δ1=∣∣ ∣∣7x2−5x+134x7∣∣ ∣∣C1↔C2Δ1=−∣∣ ∣∣x72x+1−53x47∣∣ ∣∣C2↔C3=∣∣ ∣∣x27x+13−5x74∣∣ ∣∣=Δ2⇒Δ1=Δ2 for all real x

If $Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 7 & x & 2 - 5 & x + 1 & 3 4 & x & 7 \end{matrix} ∣ ∣ ∣ ∣, Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x & 2 & 7 x + 1 & 3 & - 5 x & 7 & 4 \end{matrix} ∣ ∣ ∣ ∣$ then $Δ_{1} - Δ_{2} = 0$ for