Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Using the property of determinants and without expanding prove that determinant a-b b-c c-a b-c c-a a-b c-a a-b b-c = 0 Ex 4.2 Q : 2

Filters

Select Stream
Select Type
Select Exam
Select Subject
Select Chapter
Select Exercise
Q&A - Ask Doubts and Get Answers
Q
NCERT

Using the property of determinants and without expanding prove that determinant a-b b-c c-a b-c c-a a-b c-a a-b b-c = 0 Ex 4.2 Q : 2

Q : 2      Using the property of determinants and without expanding, prove that 

              \begin{vmatrix}a-b &b-c &c-a \\b-c &c-a &a-b \\c-a &a-b &b-c \end{vmatrix}=0

   

Answers (1)
Views
D Divya Prakash Singh

Given determinant \triangle =\begin{vmatrix}a-b &b-c &c-a \\b-c &c-a &a-b \\c-a &a-b &b-c \end{vmatrix}=0

Applying the rows addition R_{1} \rightarrow R_{1}+R_{2}   then we have;

\triangle =\begin{vmatrix}a-c &b-a &c-b \\b-c &c-a &a-b \\-(a-c) &-(b-a) &-(c-b) \end{vmatrix}=0

=-\begin{vmatrix}a-c &b-a &c-b \\b-c &c-a &a-b \\(a-c) &(b-a) &(c-b) \end{vmatrix}=0

So, we have two rows R_{1} and R_{2} identical hence we can say that the value of determinant = 0 

Therefore \triangle = 0.

 

Similar Questions

Related Chapters

Exams
Articles
Questions