Home
Class 12
MATHS
prove that [ [a-b-c , 2a , 2a ] , [2b , ...

prove that `[ [a-b-c , 2a , 2a ] , [2b , b-c-a , 2b ] ,[2c ,2c,c-a-b]]`= `(a+b+c)^3`

Text Solution

AI Generated Solution

To prove that the determinant of the matrix \[ \begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

evaluate: |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3

Using the property of determinants and without expanding, prove that: |[-a^2,a b, a c],[ b a, -b^2,b c],[c a, c b,-c^2]|=4a^2b^2c^2

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

If |(a-b-c, 2a, 2a),(2b, b-a-c, 2b),(2c, 2c, c-a-b)|=(a+b+c)(x+a+b+c)^2 then the value of x is equal to (A) -2(a+b+c) (B) a+b+c (C) -(a+b+c) (D) 2(a+b+c)

Prove the following, using properties of determinants: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3

Home
Profile