If x-22 x-33 x-4 x-42 x-93 x-16 x-82 x-273 x-64-0- then x-

The correct option is A 4 nbsp;∆=x 22x 33x 4x 42x 93x 16x 82x 273x 64=0Applying nbsp;R2→R2 R1 nbsp;and nbsp;R3→R3 R1, nbsp;we nbsp;get:∆=x 22x 33x 4 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If x-22 x-33 ...

Question

$If ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0$ , $then x$ = .

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Solution

The correct option is A 4
$Δ = ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0 Applying R_{2} \to R_{2} - R_{1} and R_{3} \to R_{3} - R_{1}, we get : Δ = ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 - 2 & - 6 & - 12 - 6 & - 24 & - 60 \end{matrix} ∣ ∣ ∣ ∣ = 0 = ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 1 & 3 & 6 1 & 4 & 10 \end{matrix} ∣ ∣ ∣ ∣ = 0 On expanding along the 1^{st} row, we get : (x - 2) \cdot 6 - (2 x - 3) \cdot 4 + (3 x - 4) \cdot 1 = 0 \Rightarrow 6 x - 12 - 8 x + 12 + 3 x - 4 = 0 \Rightarrow x = 4$

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Similar questions

Q. Find the value of x if

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

Q. Solve for

x

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

Q. The value of

x

which satisfies

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

is:

Q. Check the equality of the following determinant:

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0

Q. Show that

x - 4

is a factor of

∣ ∣ ∣ ∣ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣

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If ⎛⎜⎝x−22x−33x−4x−42x−93x−16x−82x−273x−64∣∣ ∣∣=0, then x = .

$If ⎛ ⎜ ⎝ \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 x - 4 & 2 x - 9 & 3 x - 16 x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} ∣ ∣ ∣ ∣ = 0$ , $then x$ = .