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`If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}|` then cofactor of `a_23` represented as

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If Delta=|(a_(11), a_(12), a_(13) ),(a_(21), a_(22), a_(23)),(a_(31), a_(32), a_(33))| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by (A) a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) (B) a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) (C) a_(21)A_(11)+a_(22)A_(12)+a_(23)A_(13) (D) a_(11)A_(11)+a_(21)A_(21)+a_(31)A_(31)

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by A. a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) B. a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) C. a_(21)A_(11) + a_(22)A_(12) + a_(23)A_(13) D. a_(11)A_(11) + a_(21)A_(21) + a_(31)A_(31)

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). Suppose a,b,c, in R, a+b+c gt 0, A =bc -a^(2),B =ca-b^(2) and c=ab-c^(2) and |{:(A,B,C),(B,C,A),(C,A,B):}| =49 then the valu of a^(3)+b^(3)+c^(3) -3abc is

Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

Let A=[a_(ij)]_(3xx3) be a square matrix such that A A^(T)=4I, |A| lt 0 . If |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|=5lambda|A+I|. Then lambda is equal to

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

if a_(1),a_(2),a_(3)……,a_(12) are in A.P and Delta_(1)= |{:(a_(1)a_(5),,a_(1),,a_(2)),(a_(2)a_(6),,a_(2),,a_(3)),(a_(3)a_(7),,a_(3),,a_(4)):}| Delta_(2)= |{:(a_(2)a_(10),,a_(2),,a_(3)),(a_(3)a_(11),,a_(3),,a_(4)),(a_(4)a_(12),,a_(4),,a_(5)):}| then Delta_(1):Delta_(2)= "_____"

if (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

If a_(i) , i=1,2,…..,9 are perfect odd squares, then |{:(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9)):}| is always a multiple of

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Passage Based Questions)
  1. Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+lambda z=m...

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  2. Consider the system of equations x+y+z=5, x+2y+3z=9, x+3y+lambda z=m...

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  3. If Delta=|{:(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33)...

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  4. Find |A| if A = | (5 , 2) , (6 , 3)|

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  5. If Delta=|{:(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33)...

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  6. If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 The value of ...

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  7. Let alpha,beta,gamma be the roots of x^(3)+2x^(2)-x-3=0. If the abso...

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  8. If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0. If a = al...

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  9. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

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  10. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

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  11. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

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  12. |{:(x,e^(x-1),(x-1)^(3)),(x-lnx,cos(x-1),(x-1)^(2)),(tanx,sin^(2)x,cos...

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  13. Find |A| if A = |(4x, 3x), (5x, 6x)|

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  14. Expand |(8x, 3), (2, 2)|

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  15. Let Delta = |{:(-bc,,b^(2)+bc,,c^(2)+bc),(a^(2)+ac,,-ac,,c^(2)+ac),(a^...

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  16. Expand | (7x, 4), (x, 1)|

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  17. Expand |(3,2), (1,1)|

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  18. If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in ...

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  19. Find dy/dx if x^(3)-lambdax^(2)+11x-6=y

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  20. If Deltan=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in ...

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