3 and 4 .Determinants and Matrices
hard

यदि $\left| {\,\begin{array}{*{20}{c}}{1 + ax}&{1 + bx}&{1 + cx}\\{1 + {a_1}x}&{1 + {b_1}x}&{1 + {c_1}x}\\{1 + {a_2}x}&{1 + {b_2}x}&{1 + {c_2}x}\end{array}\,} \right|$ $ = {A_0} + {A_1}x + {A_2}{x^2} + {A_3}{x^3}$ , तब ${A_1}$ का मान होगा

A

$abc$

B

$0$

C

$1$

D

इनमें से कोई नहीं

Solution

(b) $(1 + ax)\,[(1 + {b_1}x)\,(1 + {c_2}x) – (1 + {b_2}x)\,(1 + {c_1}x)]$

+ $(1 + bx)[(1 + {c_1}x)(1 + {a_2}x) – (1 + {a_1}x)\,(1 + {c_2}x)]$

+ $(1 + cx)\,[(1 + {a_1}x)\,(1 + {b_2}x) – (1 + {b_1}x)\,(1 + {a_2}x)]$

= ${A_0} + {A_1}x + {A_2}{x^2} + {A_3}{x^3}$ 

अत: हल करने के बाद $x$  का गुणांक  $  0 $ होगा।

Standard 12
Mathematics

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