यदि left| begin{array}{ccc} a^2 & b^2 & c^2 | vedclass

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(C) माना $\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 & (b + \lambda)^2 & (c + \lambda)^2 \ (a - \lambda)^2 & (b - \lambda)

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$4\lambda^2$

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(C) माना $\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 & (b + \lambda)^2 & (c + \lambda)^2 \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_2 	o R_2 - R_3$ संक्रिया लागू करने पर:$\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ (a + \lambda)^2 - (a - \lambda)^2 & (b + \lambda)^2 - (b - \lambda)^2 & (c + \lambda)^2 - (c - \lambda)^2 \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$(x + y)^2 - (x - y)^2 = 4xy$ सूत्र का उपयोग करने पर:$\Delta = \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ 4a\lambda & 4b\lambda & 4c\lambda \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_2$ से $4\lambda$ उभयनिष्ठ लेने पर:$\Delta = 4\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ (a - \lambda)^2 & (b - \lambda)^2 & (c - \lambda)^2 \end{array} ight|$.$R_3 	o R_3 - R_1 + 2\lambda R_2$ संक्रिया लागू करने पर:चूंकि $(a - \lambda)^2 = a^2 + \lambda^2 - 2a\lambda$,इसलिए $R_3 - R_1 + 2\lambda R_2 = \lambda^2$ प्राप्त होता है:$\Delta = 4\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ \lambda^2 & \lambda^2 & \lambda^2 \end{array} ight|$.$R_3$ से $\lambda^2$ उभयनिष्ठ लेने पर:$\Delta = 4\lambda^3 \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ 1 & 1 & 1 \end{array} ight|$.दिए गए समीकरण $k\lambda \left| \begin{array}{ccc} a^2 & b^2 & c^2 \ a & b & c \ 1 & 1 & 1 \end{array} ight|$ से तुलना करने पर,$k\lambda = 4\lambda^3$ प्राप्त होता है,अतः $k = 4\lambda^2$।

Similar Questions

यदि $2^{a_1}, 2^{a_2}, 2^{a_3}, \dots, 2^{a_n}$ एक $G.P.$ में हैं,तो सारणिक $\left| \begin{array}{ccc} a_1 & a_2 & a_3 \\ a_{n+1} & a_{n+2} & a_{n+3} \\ a_{2n+1} & a_{2n+2} & a_{2n+3} \end{array} \right|$ का मान क्या होगा?

यदि $\Delta = \begin{vmatrix} x+y+z^2 & x^2+y+z & x+y^2+z \\ z^2 & x^2 & y^2 \\ x+y & y+z & x+z \end{vmatrix}$,(जहाँ $x \neq y \neq z$ और $x, y, z \in \mathbb{R} - \{0\}$),तो $\Delta = $ . . . . . . .

$\left| {\begin{array}{ccc} a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c \end{array}} \right| = K \left| {\begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array}} \right|$,तो $K = $

$\left| \begin{matrix} \sin \alpha & \cos \alpha & \sin(\alpha + \gamma) \\ \sin \beta & \cos \beta & \sin(\beta + \gamma) \\ \sin \delta & \cos \delta & \sin(\delta + \gamma) \end{matrix} \right|$ का मान क्या है?

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