Using Properties of determinants, prove ...

Using Properties of determinants, prove that:
`{:|(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2{:|(a,b,c),(p,q,r),(x,y,z)|`

Promotional Banner

Promotional Banner

Topper's Solved these Questions

DETERMINANTS
OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTION -II)|3 Videos
DETERMINANTS
OSWAAL PUBLICATION|Exercise TOPIC-2 SOLUTIONS OF SYSTEM OF LINEAR EQUATIONS (LONG ANSWER TYPE QUESTIONS -II )|24 Videos
DETERMINANTS
OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (SHORT ANSWER TYPE QUESTIONS-II)|6 Videos
CONTINUITY AND DIFFERENTIABILITY
OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos
DIFFERENTIAL EQUATIONS
OSWAAL PUBLICATION|Exercise HOMOGENEOUS DIFFERENTIAL EQUATIONS (Long Answer Type Questions - III)|8 Videos

Similar Questions

Explore conceptually related problems

|(b+c, q+r, y+z),(c+a,r+p,z +x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

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

Using the property of determinants and without expanding {:|( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) |:}=2 {:|(a,p,x),( b,q,y),(c,r,z)|:}

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(ax^2+b,cx^2+d,px^2+q),(u,v,w)|=(x^4-1){:|(b,d,q),(a,c,p),(u,v,w)|

Prove that Delta ={:|( a+bx,c+dx,p+qx),( ax+b,cx+d,px+q),(u,v,w) |:}=( 1-x^(2)) {:|( a,c,p),(b,d,q),(u,v,w)|:}

Prove that |(a+bx ,c+dx,p+qx),(ax + b, cx +d, px +q),(u,v,w)|= (1- x^3) |(a,c,p),(b,d,q),(u,v,w)|

|(x,a,x+a),(y,b,y+b),(z,c,z+c)| = 0

Prove that |{:(,x+y+2z,x,y),(,z,y+z+2z,y),(,z,x,z+x+2y):}|=2(x+y+z)^(3) .

Prove that |(x,p,q),(p,x,q),(p,q,x)| = (x - p)(x - q)(x + p +q)

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)

Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^...
Text Solution
|
Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...
Text Solution
|
Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...
Text Solution
|
IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...
Text Solution
|
Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)
Text Solution
|
Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...
Text Solution
|
Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...
Text Solution
|
Find the equation of the line joining A( 1,3) and B (0,0) using det...
Text Solution
|
Using properties of determinants, prove the following: |xx+y x+2y\...
Text Solution
|
Using properties of determinants, prove the following: |alphabetag...
Text Solution
|
15. Using properties of determinants, prove the following |[a,b,c],[a-...
Text Solution
|
[[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3
Text Solution
|
Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...
Text Solution
|
Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...
Text Solution
|
Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...
Text Solution
|
Using the Properties of determinants, prove that following: {:|(-a^2...
Text Solution
|
Using the Properties of determinants, prove the following: {:|(1,1...
Text Solution
|
If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...
Text Solution
|
Using properties of determinants, solve the following for x: |x-2 ...
Text Solution
|
Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...
Text Solution
|