Generalized Inverse Pada Matriks Atas Zn

Abstract

Suatu matriks mempunyai invers apabila matriks tersebut non-singular dan bujur sangkar. Namun, apabila matriks tersebut singular atau tidak bujur sangkar, inversnya masih dapat ditentukan dengan generalized inverse. Pada tugas akhir ini dibahas bagaimana menentukan generalized inverse pada matriks atas menggunakan aturan algoritma dan aturan pendiagonalan matriks. Berdasarkan pembahasan pada tugas akhir ini dapat disimpulkan bahwa apabila merupakan bilangan prima makaadalah lapangan dan matriks atas pasti mempunyai generalized inverse. Namun apabila bukan bilangan prima maka adalah ring komutatif dengan elemen satuan dan matriks atas mempunyai generalized inverse apabila dalam proses pengerjaan tidak dibutuhkan invers dari suatu elemen atas yang tidak mempunyai invers terhadap perkalian. Adapun generalized inverse yang diperoleh adalah tidak tunggal.

Application of the Leslie Matrix to Predict the Number and Growth Rate of Women in West Java 2021

“…So that for next year, the population growth model is as in equation ( 15 (Marzuki et al, 2017). The female population can be grouped by age class as in Table 4.…”

“…It is defined i b as the survival rate of women in age class i , which is the chance for women to survive from age class i until 1 i  at time to t . Here is the general form of the Leslie matrix is stated (Marzuki et al, 2017):…”

“…In population growth, there are several factors that very give effect, which is the level of fertility, the level of life survival and the age range of the population. This population growth can provide information on how much changes in population numbers for the next year (Marzuki et al, 2017). Data from the Central Statistics Agency 2019 collected that the total population of female in Indonesia is less than male which is 131.48 million people if compared to the total male population which is 132.68 million people.…”

“…The targets of the development plan contained in the 2005-2025 RPJM is to improve the quality of human resources including the role of women in development (BPS, 2019). The growth of the female population is an important thing that must be observed, considering the role of women is determining development the human population in the future, because without the role of women, the population will not be able to develop (Marzuki et al, 2017). Research using the Leslie Matrix on fertility has been carried out in China which aims to determine the impact of changes in fertility policy in China on the UEBMI fund balance.…”