Programme Code : BDP
Course Code : BECE-15
|

Year : 2013 Views: 2443 Submitted By : Prity On 30th March, 2013

Q.

Define

a. Adjugate of a matrix

b. Decomposable matrix

c. Singular matrix

### Catch The Solution

 By vidhi Adjoint or Adjugate The adjoint of A, ADJ(A) is the transpose of the matrix formed by taking the cofactor of each element of A. ADJ(A) A = det(A) I If det(A) != 0, then A-1 = ADJ(A) / det(A) but this is a numerically and computationally poor way of calculating the inverse. ADJ(AT)=ADJ(A)T ADJ(AH)=ADJ(A)H A matrix, A, is fully decomposable (or reducible) if there exists a permutation matrix P such that PTAP is of the form [B C; 0 D] where B and D are square. A matrix, A, is partly-decomposable if there exist permutation matrices P and Q such that PTAQ is of the form [B C; 0 D] where B and D are square. A matrix that is not even partly-decomposable is fully-indecomposable. A matrix is singular if it has no inverse. A matrix A is singular iff det(A)=0. A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that if you pick a random square matrix over a continuous uniform distribution on its entries, it will almost surely not be singular.

 Q 13. If Z = f(x,y) = xy Find the maximum value for f(x,y) if x & y are constrained to sum to 1 (That is x+y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian ... Prity    30th March, 2013 Hits: 983