Cofactor of an element in the `i^(th)` row and `j^(th)` column =

The cofactor of an element in the i^(th) row and the j^(th) column of a 3times3 matrix is defined

Consider the determinant, Delta=|(p,q,r),(x,y,z),(l,m,n)| . M_(ij) denotes the minor of an element in i^(th) row, and j^(th) column C_(ij) denotes the cofactor of an element in i^(th) row and j^(th) column The value of p.C_21+q.C_22+r.C_23 is :

Consider the determinant, Delta=|(p,q,r),(x,y,z),(l,m,n)| . M_(ij) denotes the minor of an element in i^(th) row, and j^(th) column C_(ij) denotes the cofactor of an element in i^(th) row and j^(th) column The value of x.C_21+y.C_22+z.C_23 is :

Consider the determinant, Delta=|(p,q,r),(x,y,z),(l,m,n)| . M_(ij) denotes the minor of an element in i^(th) row, and j^(th) column C_(ij) denotes the cofactor of an element in i^(th) row and j^(th) column the value of q.M_12 - y.M_22+ m.M_32 is :

In a third order matrix A, a_(ij) denotes the element in the i^(th) row and j^(th) column. If a_(ij) = {{:(0,"for I"= j),(1,"for I" gt j),(-1,"for I"lt j):} then the matrix is

The element in the i^(th) row and the j^(th) column of a determinant of third order is equal to 2(i+j) . What is the value of the determinant?

Construct a 3xx2 matrix whose elements in the ith row and jth column are given by : a_(ij)=(i+4j)/(2)

Let A = [a_(ij)] be 3 xx 3 matrix given by a_(ij) = {(((i+j)/(2))+(|i-j|)/(2),if i nej,),((i^(j)-(i.j))/(i^(2)+j^(2)),if i n=j,):} where a_(ij) denotes element of i^(th) row and j^(th) column of matrix A. On the basis of above information answer the following question: If a 3 xx3 matrix B is such that A^(2) +B^(2) = A +B^(2)A , then det. (sqrt(2)BA^(-1)) is equal to

Let A = [a_(ij)] be 3 xx 3 matrix given by a_(ij) = {(((i+j)/(2))+(|i-j|)/(2),if i nej,),((i^(j)-(i.j))/(i^(2)+j^(2)),if i =j,):} where a_(ij) denotes element of i^(th) row and j^(th) column of matrix A . On the basis of above information answer the following question: If A^(2)+ pA + qI_(3) = 32 A^(-1) , then (p +q) is equal to-

A is a matrix of 3xx3 and a_(ij) is its elements of i^(th) row and j^(th) column. If a_(ij)+a_(jk)+a_(ki)=0 holds for all 1 le i, j, kle 3 then