Matrices Essay Example | Topics and Well Written Essays - 500 words

Lattices - Essay Example It stays to decide whether any of the 33 sub lattices of the expanded framework (B) have a non †zero determinant. For instance in a square sub grid of request 33 of [B], to be specific, These arrangement of conditions are conflicting, on the grounds that the position of the coefficient grid [A] in which det(D) = 0. Also, a third request square sub lattices of [B], specifically, , and are with the end goal that their comparing determinants are zero. At the end of the day, all the third request square sub lattices of the enlarged network [B] have a zero determinant. In this manner, the position of the expanded grid [B] is under 3. Since, there exists a second request square sub lattice of grid [B], with the end goal that det(H) = - 120≠0, the position of the expanded framework [B] is 2. The position of the coefficient framework [A], whereis to be resolved. Det(A) = 0. Subsequently, the position of the coefficient lattice [A] is under 3. is a square sub network of lattice [A] and det (J) = - 3 ï‚ ¹ 0. Hence, the position of the coefficient lattice [A] is 2. Thus, rank of the coefficient network [A] = rank of the expanded grid [B], as needs be the arrangement of conditions given by [A] [X] = [B] is predictable. In any case, the position of the coefficient framework [A] = rank of the expanded lattice [B] < 3, in this manner there are just 2 requirements; thus, these conditions have boundlessly numerous