On expanding by first row, the value of the determinant of `3xx3` square matrix `A=[a_(i j)]` is `a_(11)C_(11)+a_(12)C_(12)+a_(13)C_(13)+a_(32)C_(32)+a_(33)C_(33)` .

Find minors and cofactors of the elements a_(11), a_(21) in the determinant Delta=|a_(11)a_(12)a_(13)a_(21)a_(22)a_(23)a_(31)a_(32)a_(23)|

Find minors and cofactors of the elements of the determinant |2-3 5 6 0 4 1 5-7| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

The square matrix A=[a_(ij)" given by "a_(ij)=(i-j)^3 , is a

For a 2^(nd) order determinant abs(A)=abs(a_(ij)) , find a_(12)A_(11)+a_(22)A_(21)

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)

Construct a matrix [a_(ij)]_(3xx3) , where a_(ij)=2i-3j .

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

The determinant |(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2)),(b_(3)+c_(3),c_(3)+a_(3),a_(3)+b_(3))|

Construct a matrix [a_(ij)]_(3xx3) ,where a_(ij)=(i-j)/(i+j).