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Use the properties of determinant and wi...

Use the properties of determinant and without expanding prove that `|{:(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):}|`.

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

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

Without expanding, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),(x+y,y+z,z+x):}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

Without expansion, prove the following: |(a+b, b+c, c+a),(p+q, q+r, r+ p),(x+y, y+z, z+x)|=2|(a,b,c),(p,q,r),(x,y,z)|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

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]|

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Use the properties of determinant and without expanding prove that |{...

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  2. If a^(2)+b^(2)+c^(2)=-2 and f(x)= |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x...

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  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

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  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

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  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

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  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

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  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

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  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

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  11. If the trivial solution is the only solution of the system of equation...

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  12. The number of values of k, for which the system of equations (k""+"...

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  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

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  14. The set of the all values of lamda for which the system of linear equa...

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  15. Which of the following values of alpha satisfying the equation |(1+alp...

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  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

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  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

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  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

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  19. If S is the set of distinct values of ' b for which the following syst...

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