Using the properties of determinants, pr...

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`

`-(a+b+c)`

`2(a+b+c)`

abc

`-2(a+b+c)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

JEE 2019
CENGAGE PUBLICATION|Exercise Chapter 1|5 Videos
JEE 2019
CENGAGE PUBLICATION|Exercise Chapter 2|7 Videos
JEE 2019
CENGAGE PUBLICATION|Exercise chapter -3|1 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
CENGAGE PUBLICATION|Exercise All Questions|541 Videos
LIMITS
CENGAGE PUBLICATION|Exercise Comprehension Type|4 Videos

Similar Questions

Explore conceptually related problems

By using properties of determinants , show that : (i) {:|( a-b-c, 2a, 2a),( 2b, b-c-a, 2b ) , ( 2c,2c, c-a-b) |:} = ( a+b+c)^(3) (ii) {:|( x+y+2z, x,y ),( z, y+z+2x, y ),( z,x,z+x+2y )|:} =2( x+y+z)^(3)

Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

Using the property of determinants and without expanding {:|( a-b,b-c, c-a),( b-c,c-a,a-b),( c-a,a-b,b-c)|:} =0

Using properties of determinants prove that, |{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}|=2abc(a+b+c)^(3)

Using properties of determinant prove that |[a+b+c,-c,-b],[-c, a+b+c,-a],[-b,-a, a+b+c]|=2(a+b)(b+c)(c+a)

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

prove that, |{:(" "2a,a-b-c," "2a),(" "2b," "2b,b-c-a),(c-a-b," "2c," "2c):}|=(a+b+c)^3

Prove that, |{:(6a,a,a),(12b,2b,2b),(9c,c,-2c):}|=0

Without expanding the determinant, prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

CENGAGE PUBLICATION-JEE 2019-MCQ

If the system of linear equations x-4y+7z=g, 3y-5z=h, -2x+5y-9z=k is c...
Text Solution
|
If the system of equations x+y+z = 5 x + 2y + 3z = 9 x + 3y + a...
Text Solution
|
Let a(1),a(2),a(3), …, a(10) be in G.P. with a(i) gt 0 for i=1, 2, …, ...
Text Solution
|
If the system of linear equations 2x+2y+3z=a 3x-y+5z=b x-3y+2z=...
Text Solution
|
Using the properties of determinants, prove that following |(a-b-c,2a,...
Text Solution
|
An ordered pair (alpha, beta) for which the system of linear equations...
Text Solution
|
The set of all values of lambda for which the system of linear equatio...
Text Solution
|
If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...
Text Solution
|
Matrix=[[e^t,e^-t(sint-2cost),e^-t(-2sint-cost)],[e^t,-e^-t(2sint+cost...
Text Solution
|
Let d in R and A= ((-2,4+d, sintheta-2),(1, sintheta+2,d),(5, 2sinthet...
Text Solution
|
Let A=[(2,b,1),(b,b^(2)+1,b),(1,b,2)] where b gt 0. Then the minimum v...
Text Solution
|
Let A=[[0,2q,r] , [p,q,-r] , [p,-q,r]] If A A^T=I3 then |p|=
Text Solution
|
Let A and B be two invertible matrices of order 3xx3. If det. (ABA^(T)...
Text Solution
|
Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...
Text Solution
|
If A = [(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)], then ...
Text Solution
|
Two cards are drawn successively with replacement from a well-shuffled...
Text Solution
|
An urn contains 5 red and 2 green balls. A ball is drawn at random fro...
Text Solution
|
An unbiased coin is tossed. If the result is a head, a pair of unbi...
Text Solution
|
If the probability of hitting a target by a shooter, in any shot is 1/...
Text Solution
|
In a random experiment, a fair die is rolled until two fours are obtai...
Text Solution
|