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Let a-2b+c=1.  If f\left ( x \right )= \begin{vmatrix} x+a & x+2 &x+1 \\ x+b &x+3 &x+2 \\ x+c &x+4 & x+3 \end{vmatrix}, then :   
Option: 1 f(-50)=501
Option: 2 f(-50)=-1
Option: 3 f(50)=1
Option: 4 f(50)=-501

Answers (1)




Elementary row operations -

Elementary row operations

Row transformation: Following three types of operation (Transformation) on the rows of a given matrix are known as elementary row operation (transformation).

    i) Interchange of ith row with jth row, this operation is denoted by 

        \\\mathrm{R_i \leftrightarrow R_j \;\;or\; R_{ij}}

    ii) The multiplication of ith row by a constant k (k≠0) is denoted by

         \\\mathrm{R_i \leftrightarrow kR_i \;\; or \; k\cdot R_i}    

    iii) The addition of ith row to the elements of jth row multiplied by constant k (k≠0) is denoted by

        \\\mathrm{R_i \leftrightarrow R_i + kR_j \;\; or \; k\cdot R_{ij}}

In the same way, three-column operations can also be defined too.




\\\text { Apply } \mathrm{R}_{1}=\mathrm{R}_{1}+\mathrm{R}_{3}-2 \mathrm{R}_{2}\\\Rightarrow f(x)=\left|\begin{array}{ccc}{1} & {0} & {0} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right| \quad \Rightarrow f(x)=1 \\\quad \Rightarrow f(50)=1

Correct Option (3)

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