Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Solve the equation determinant x + a x x x x + a x x x x + a equals 0; a not equal to 0.

Q : 5        Solve the equation     

                 \begin{vmatrix} x+a & x &x \\ x &x+a &x\\ x & x & x+a \end{vmatrix}=0; a\neq 0

Answers (1)

best_answer

Given determinant \begin{vmatrix} x+a & x &x \\ x &x+a &x\\ x & x & x+a \end{vmatrix}=0; a\neq 0

Applying the row transformation; R_{1} \rightarrow R_{1}+R_{2}+R_{3} we have;

\begin{vmatrix} 3x+a & 3x+a &3x+a \\ x &x+a &x\\ x & x & x+a \end{vmatrix} =0

Taking common factor (3x+a) out from first row.

(3x+a)\begin{vmatrix} 1 & 1 &1 \\ x &x+a &x\\ x & x & x+a \end{vmatrix} =0

Now applying the column transformations; C_{1} \rightarrow C_{1}-C_{2} and C_{2} \rightarrow C_{2}-C_{3}.

we get;

(3x+a)\begin{vmatrix} 0 & 0 &1 \\ -a &a &x\\ 0 & -a & x+a \end{vmatrix} =0

=(3x+a)(a^2)=0           as    a^2 \neq 0,

or 3x+a=0  or   x= -\frac{a}{3}

Posted by

Divya Prakash Singh

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Result 2025 Live: UK Board 10th, 12th results tomorrow; AP SSC, TS Inter, UP, CBSE updates
anam-khan

When will CBSE Class 12 results 2025 be declared? Last two years' trends

Latest Question