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

Matrices - Essay Example It remains to determine if any of the 33 sub matrices of the augmented matrix (B) have a non – zero determinant. For example in a square sub matrix of order 33 of [B], namely, These system of equations are inconsistent, because the rank of the coefficient matrix [A] in which det(D) = 0. Moreover, a 3rd order square sub matrices of [B], namely, , and are such that their corresponding determinants are zero. In other words, all the 3rd order square sub matrices of the augmented matrix [B] have a zero determinant. Therefore, the rank of the augmented matrix [B] is less than 3. Since, there exists a 2nd order square sub matrix of matrix [B], such that det(H) = -120≠ 0, the rank of the augmented matrix [B] is 2. The rank of the coefficient matrix [A], whereis to be determined. Det(A) = 0. Hence, the rank of the coefficient matrix [A] is less than 3. is a square sub matrix of matrix [A] and det (J) = -3 ï‚ ¹ 0. Therefore, the rank of the coefficient matrix [A] is 2. Hence, rank of the coefficient matrix [A] = rank of the augmented matrix [B], accordingly the system of equations given by [A] [X] = [B] is consistent. Nevertheless, the rank of the coefficient matrix [A] = rank of the augmented matrix [B] < 3, therefore there are only 2 constraints; consequently, these equations have infinitely many