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This is the determinant, pls help me in evaluating this determinant |1 a axa | |1 b bxb | |1 c cxc | {x is nothing but multiplication}

This is the determinant, pls help me in evaluating this determinant
|1 a axa |
|1 b bxb |
|1 c cxc |
{x is nothing but multiplication}

Grade:10

2 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

Dear Aditya

Your quetion is not clear in the sense axa can be written as x*a^2. Such type of quetions can be solved by applying row operations i.e. R3 =R3-R2   and R2=R2-R1. Then it will be quite easy to solve the determinant.

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

 

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Rubankumar S
14 Points
10 years ago

 

 

 

 

 

 

 

 

 

 

 

 

 

|1   a   a^2|

|1   b    b^2|

|1  c  c^2|

 

=  0   a-b     a^2 - b^2            here i am not usin paranthesis it is impossible for me to use so i left it.but you should use

    0   b-c      b^2 - c^2            R1=R1- R2      R2=R- R        BY DOING SO VALUE OF DET DOESN'T CHANGE

    1   c         c^2

 

=  (a-b)(b-c) *        0  1    a+b              take (a-b) from R1  ;(b-c) from R2

                             0  1    b+c

                              1  c    c^2

= (a-b)(b-c)  *{1(b+c)-(a+b)}               expand det along C1

= (a-b)(b-c)(c-a)

 

 

 

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