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If Delta=|{:(a(11),a(12),a(13)),(a(21),a...

`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 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

if a_(1)b_(1)c_(1), a_(2)b_(2)c_(2)" and " a_(3)b_(3)c_(3) are three-digit even natural numbers and Delta = |{:(c_(1),,a_(1),,b_(1)),(c_(2),,a_(2),,b_(2)),(c_(3),,a_(3),,b_(3)):}|" then " Delta is

Knowledge Check

  • If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and A_(ij) is Cofactor of a_(ij) , 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)`

  • Delta=|(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))| and A_(ij) is cofactor of a_(ij) 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)+aB_(3)A_(3)`
    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 = abs{:(a_11, a_12, a_13),(a_21, a_22, a_23),(a_31, a_32, a_33):} and A_(ij) are cofactors of a_(ij) 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)`

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    Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 Let d_(i) be the common difference of the elements in with row then sum_(i=1)^(n)d_(i) is

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    Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 .Let Di be the common difference of i^(th) row The value of lim_(nto oo)sum_(i=1)^(n)D_(i) is equal to

    If Delta = abs{:(a_11, a_12, a_13),(a_21, a_22, a_23),(a_31, a_32, a_33):} and A_(ij) are cofactors of a_(ij) then value of Delta is given by

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