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

Self-Analysis of Leadership Abilities Essay Example | Topics and Well Written Essays - 1250 words

Self-Analysis of Leadership Abilities - Essay Example This paper discusses that  the leadership style survey test helped to assess the leadership style I normally operated out of.   After taking the self-assessment test, I computed my highest score to be that of a participative or democratic leader.   Clark explained that the best leaders â€Å"operate out of the participative mode and use the other two modes as needed†.   He cites an instance when the firm would have a new crew or a temporary work force.   Such a leader has to practice a more authoritarian type of leadership in order to get the crew to work efficiently. But for a leader who is already working with professionals or a crew which knows more about the work than he does, then a leader can best apply a delegative style of leadership.   For these instances, a participative leader makes the necessary adjustments in leadership styles based on the situation he or she is faced with.This study declares that  for the leaders who want their members to grow beyon d their employee status and knowledge, the participative leadership style helps these employees adjust and grow into their jobs.   In the interim, these employees are usually given more authority over their jobs.  Some leaders may exemplify with an impoverished leadership style, where they are weak on both tasks and on people skills; some may be authoritarian, where they are strong on tasks and weak on people skills; some may be socialites and be weak on tasks and strong on people skills; and the rest may be on the middle-of-the-road leaders, and with more experience can later manifest with good team leadership skills.