If `A= (a_(ij))` is a `4xx4` matrix and `C_(ij)`, is the co-factor of the element `a_(ij)`, in `Det (A)`, then the expression `a_11C_11+a_12C_12+a_13C_13+a_14C_14` equals-

Let A=[a_(ij)]_(nxxn) be a square matrix and let c_(ij) be cofactor of a_(ij) in A. If C=[c_(ij)] , then

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)|

Construct 3xx4 matrix A=[a_(aj)] whose elements are: a_(ij)=i.j

Let A=[a_("ij")] be 3xx3 matrix and B=[b_("ij")] be 3xx3 matrix such that b_("ij") is the sum of the elements of i^(th) row of A except a_("ij") . If det, (A)=19 , then the value of det. (B) is ________ .

Construct 3xx4 matrix A=[a_(aj)] whose elements are: a_(ij)=i/j

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)

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals

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 _______.

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlemin{m,n} (C) r=min{m,n} (D) none of these

If A=[a_(ij)]_(mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemin{m,n} (C) rltmin{m,n} (D) none of these