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If Delta=|a(11)a(12)a(13)a(21)a(22)a(23)...

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

A

`a_(11)A_(31)+a_(12)+A_(32)+a_(12)A_(33)`

B

`a_(11)A_(11)+a_(12)+A_(21)+a_(13)A_(33)`

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)`

Text Solution

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The correct Answer is:
B
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(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

Find minors and cofactors of the elements of the determinant det[[2,-3,56,0,41,5,-7]]a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

Knowledge Check

  • 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)

    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 A=[{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}] and A_(ij) is co-factos of a_(ij) , then A 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_(33)`
    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 A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and A_(ij) denote the cofactor of element a_(ij) , then a_(11)A_(21)+a_(12)A_(22)+a_(13)A_(23)=

    A
    `0`
    B
    `|A|`
    C
    `-|A|`
    D
    `2|A|`

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