If begin vmatrix 2 x - 5 18 - xlend vmatrix - begin vmatrix 6 -2 7 - 3lend vmatrix - then the value of x isa 3b - 3c - 6d 6

(c) ∵ 2x amp; 5 8 amp; x = 6 amp; 2 7 amp; 3 ⇒ 2x^2 40=18+14 ⇒ 2x^2=32+40 ⇒ x^2=72/2=36 ∴ x = ± 6 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If begin vmat...

Question

If $∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣$ , then the value of x is

(a) $3$
(b) $\pm 3$
(c) $\pm 6$
(d) $6$

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Solution

(c) $∵ ∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣$
$\Rightarrow 2 x^{2} - 40 = 18 + 14 \Rightarrow 2 x^{2} = 32 + 40 \Rightarrow x^{2} = \frac{72}{2} = 36 ∴ x = \pm 6$

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Similar questions

If $∣ ∣ ∣ \begin{matrix} x & 2 18 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & 2 18 & 6 \end{matrix} ∣ ∣ ∣$ , then x is equal to
a) 6
b) $\pm 6$
c) -6
d) zero

Q. The value of

x,

∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & 5 8 & 3 \end{matrix} ∣ ∣ ∣

Q. If

∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣

, write the value of

x .

Q. Find the values of

x

, if
(i)

∣ ∣ ∣ \begin{matrix} 2 & 4 5 & 1 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 2 x & 4 6 & x \end{matrix} ∣ ∣ ∣

(ii)

∣ ∣ ∣ \begin{matrix} 2 & 3 4 & 5 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} x & 3 2 x & 5 \end{matrix} ∣ ∣ ∣

Q. Find the value of

x

∣ ∣ ∣ \begin{matrix} 2 & 4 5 & 1 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 2 x & 4 6 & x \end{matrix} ∣ ∣ ∣

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If ∣∣∣2x58x∣∣∣=∣∣∣6−273∣∣∣, then the value of x is (a) 3 (b) ±3 (c) ±6 (d) 6

(c) ∵∣∣∣2x58x∣∣∣=∣∣∣6−273∣∣∣ ⇒2x2−40=18+14⇒2x2=32+40⇒x2=722=36∴x=±6

If $∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣$ , then the value of x is

(a) $3$
(b) $\pm 3$
(c) $\pm 6$
(d) $6$

(c) $∵ ∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣$
$\Rightarrow 2 x^{2} - 40 = 18 + 14 \Rightarrow 2 x^{2} = 32 + 40 \Rightarrow x^{2} = \frac{72}{2} = 36 ∴ x = \pm 6$