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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|`

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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|

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)|

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|

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|

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]|

Show 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|

Using the property of determinants and without expanding, prove that: |[x, a ,x+a],[ y, b, y+b],[ z, c, z+c]|=0

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

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):}|

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

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  2. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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  3. The value of |alpha| for which the system of equation alphax+y+z=alpha...

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  4. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

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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 for which the linear equations 4x+ky+2...

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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 , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

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  14. The set of all values of lambda for which the system of linear equ...

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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-lam...

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  17. The total number of distinct x in R for which |{:(x,,x^(2),,...

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  18. Let alpha, lambda , mu in R.Consider the system of linear equations ...

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

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