Judul: Invers dari Matriks Tridiagonal Jacobi
Abstrak: Suatu matriks berukuran n×n dinamakan matriks tridiagonal jika untuk . Karya ilmiah ini memberikan algoritma yang mudah untuk menemukan invers ( dari matriks tridiagonal Jacobi yang simetrik dan nonsimetrik. Setiap elemen pada matriks tridiagonal ini adalah bilangan real. Terdapat 3 lema dan 2 teorema untuk menentukan . Lema pertama menunjukkan persamaan utama dalam membuktikan lema-lema dan teorema-teorema selanjutnya. Invers dari matriks yang simetrik dibuktikan oleh lema kedua yang menunjukkan elemen-elemen baris ke- dari . Selanjutnya, lema kedua dilengkapi dengan teorema pertama yang menunjukkan elemen-elemen dengan . Invers dari matriks yang nonsimetrik dibuktikan oleh lema ketiga yang menunjukkan elemen-elemen dengan dan elemen-elemen dengan dibuktikankan oleh teorema kedua.
Keyword: symmetric, nonsymmetric, matrix

Judul: Determinan dan Invers Matriks Toeplitz Tridiagonal
Abstrak: Matriks merupakan susunan dari bilangan-bilangan yang diatur dalam kolom dan baris yang berbentuk persegi atau persegi panjang, salah satu jenis matriks adalah matriks Toeplitz. Matriks Toeplitz adalah matriks simetrik yang setiap unsur pada diagonal utamanya sama, dan setiap unsur pada subdiagonal yang bersesuaian dengan diagonal utama juga sama. Pada karya ilmiah ini diformulasikan cara hitung efisien untuk menentukan determinan dan invers matriks Toeplitz Tridiagonal. Formulasi determinan diberikan dalam bentuk eksplisit dan rekursif. Rumusan eksplisit diturunkan mengikuti pola binomial dan dibuktikan secara induktif. Sedangkan formula rekursif diperoleh dari mengamati struktur entri matriks tersebut. Pada akhirnya, formula rekursif ini menjadi dasar untuk merumuskan cara menghitung invers matriks Toeplitz Tridiagonal yang efisien., A matrix is an arrangement of numbers arranged in columns and rows in the form of a square or rectangle, one type of matrix is the Toeplitz matrix. The Toeplitz matrix is a symmetric matrix in which every element on the main diagonal is the same, and every element in the subdiagonal corresponding to the main diagonal is also the same. In this scientific paper, an efficient calculation method is formulated to determine the determinant and the inverse of the Tridiagonal Toeplitz matrix. The determinant formulation is given in an explicit and a recursive form. The explicit formula is derived from binomial patterns and the proof is based on inductive method. While the recursive formula is obtained from observing the structure of the matrix entry. In the end, this recursive formula becomes the basis for formulating an efficient way to calculate the inverse of the Tridiagonal Toeplitz matrix.
Keyword: Determinan, Invers, Matriks Toeplitz

Judul: Application of steel slag, dolomite, silica gel, and micro fertilizer in rice plant on peat soil
Abstrak: Steel slag as a by-product formed in the process of steel manufacturing consists of iron-making slag or blast furnace slag (BFS) and steel-making slag or electric furnace slag (EFS) had been used as Si fertilizer and liming materials. Steel slag containing silicate, micro elements, and bases can be used to improve chemical properties of peat soil that are poor in nutrients. Steel slag contains a lot of silicate needed by especially Si accumulator plants such as paddy rice plant. This research aimed to compare paddy rice plant’s response of IR64 and Air Tenggulang to EF slag, BF slag, dolomite, silica gel and micro fertilizer application for improving chemical properties of peat soil, to know the reason of paddy rice plant’s response on peat soil to steel slag application and to evaluate steel slag effect in content of hazardous heavy metal in brown rice. This research consisted of an incubation and a greenhouse experiments. Both of them were single factor experiment arranged in a completely randomized design. The treatments were both EFS and BFS (0%, 2%, 4%, 6%, 8% w/w of the soil), both dolomite and silica gel equivalent EFS dosage and also micro nutrients with three replications. The results showed that application of EFS on peat soil significantly improved the availability of Fe and Mn, BFS on peat soil significantly improved the availability of Si and Mg and dolomite on peat soil significantly improved soil pH and availability of Ca. Paddy rice grown on peat soil highly responded to steel slag application. Plant height, number of tillers, weight of spikilets, SiO2 of straw were significantly raised with EFS application and content of hazardous heavy metal in brown rice still within limit of food maximum pollution, but Pb and Hg were not detected. In general, the highest rice yield was achieved at dosage of EFS 8%. In conclusion, paddy rice grown responded to steel slag application was associated in increasing soil pH, the availability of Ca, Mg, Fe, Mn and Si on peat soil. Generally, Paddy rice grown on peat soil highly responded to EFS application better than the others. It meaned that not only silicate as the main factor in improving peat soil chemistry and rice yield, but also increasing soil pH, availability of Ca, Mg and micro nutrients.
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