PROFIL KESALAHAN SISWA DALAM MENYELESAIKAN SOAL MATRIKS BERDASARKAN JENIS KELAMIN DI SMA NEGERI 7 PALU

Abstrak: Penelitian ini merupakan penelitian kualitatif yang bertujuan untuk memperoleh profil kesalahan yang dilakukan siswa dalam menyelesaikan soal matriks berdasarkan jenis kelamin di SMA Negeri 7 Palu. Data dikumpulkan dengan cara metode tes dan wawancara. Subjek penelitian terdiri dari satu siswa laki-laki (SH) dan satu siswa perempuan (DS). Hasil Penelitian menunjukkan bahwa kesalahan konseptual yang dilakukan siswa laki-laki (SH) yaitu : 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan tidak menerapkan rumus invers, 4) kesalahan konsep invers matriks dan 5) kesalahan konsep adjoin. Kesalahan prosedural yang dilakukan siswa laki-laki berupa 1) kesalahan dalam melakukan perhitungan, 2) kesalahan tidak menyederhanakan dan 3) kesalahan tidak menuliskan tanda operasi pada matriks. Sedangkan kesalahan konseptual yang dilakukan siswa perempuan (DS) yaitu: 1) kesalahan tidak memahami konsep rumus perkalian matriks, 2) kesalahan konsep perkalian matriks, 3) kesalahan konsep adjoin dan 4) kesalahan konsep invers matriks. Kesalahan prosedural yang dilakukan siswa perempuan berupa 1) kesalahan dalam melakukan perhitungan. Siswa laki-laki banyak melakukan kesalahan dari pada siswa perempuan dikarenakan, siswa laki-laki tidak teliti dan terburu-buru dalam menyelesaikan soal matriks. Sedangkan siswa perempuan tidak terlalu banyak melakukan kesalahan dikarenakan cenderung lebih teliti dan cermat dalam menyelesaikan soal matriks. Kata kunci: Profil Kesalahan, Jenis Kelamin dan Matriks Abstract: This research is a qualitative research which aims to obtain a profile of errors students make in solving matrix problems based on sex in SMA 7 Palu. Data was collected by means of test and interview methods. The research subjects consisted of one male student (SH) and one female student (DS). The results showed that the conceptual errors made by male students (SH) were: 1) errors not understanding the concept of matrix multiplication formula, 2) errors in matrix multiplication concepts, 3) errors not applying inverse formulas, 4) inverse matrix concept errors and 5 ) the error of the adjoin concept. Procedural errors made by male students in the form of 1) errors in making calculations, 2) errors do not simplify and 3) errors do not write the operation mark on the matrix. Whereas the conceptual errors made by female students (DS) are: 1) errors do not understand the concept of matrix multiplication formula, 2) errors in the concept of matrix multiplication, 3) errors in adjoining concepts and 4) inverse matrix concept errors. Procedural errors made by female students in the form of 1) errors in carrying out calculations. Male students make a lot of mistakes than female students because , male students are not careful and in a hurry to solve the matrix problem. Whereas female students don't make too many mistakes becausethey tend to be more thorough and careful in solving matrix problems. Keywords: Error Profile, Gender and Matrix

Multiplication Formulas and Canonical Bases for Quantum Affine gln

We will give a representation-theoretic proof for the multiplication formula in the Ringel-Hall algebra of a cyclic quiver Δ(n). As a first application, we see immediately the existence of Hall polynomials for cyclic quivers, a fact established by J. Y. Guo and C. M. Ringel, and derive a recursive formula to compute them. We will further use the formula and the construction of a monomial basis for given by Deng, Du, and Xiao together with the double Ringel-Hall algebra realisation of the quantum loop algebra given by Deng, Du, and Fu to develop some algorithms and to compute the canonical basis for . As examples, we will show explicitly the part of the canonical basis associated with modules of Lowey length at most 2 for the quantum group .

The M-intersection graph of ideals of a commutative ring

Let [Formula: see text] be a commutative ring and [Formula: see text] be an [Formula: see text]-module, and let [Formula: see text] be the set of all nontrivial ideals of [Formula: see text]. The [Formula: see text]-intersection graph of ideals of [Formula: see text], denoted by [Formula: see text], is a graph with the vertex set [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. For every multiplication [Formula: see text]-module [Formula: see text], the diameter and the girth of [Formula: see text] are determined. Among other results, we prove that if [Formula: see text] is a faithful [Formula: see text]-module and the clique number of [Formula: see text] is finite, then [Formula: see text] is a semilocal ring. We denote the [Formula: see text]-intersection graph of ideals of the ring [Formula: see text] by [Formula: see text], where [Formula: see text] are integers and [Formula: see text] is a [Formula: see text]-module. We determine the values of [Formula: see text] and [Formula: see text] for which [Formula: see text] is perfect. Furthermore, we derive a sufficient condition for [Formula: see text] to be weakly perfect.

The derivative and tangent operators of a motion in Lorentzian space

In this paper, by using Lorentzian matrix multiplication, [Formula: see text]-Tangent operator is obtained in Lorentzian space. The [Formula: see text]-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. [Formula: see text]-Tangent operators are related to vectors. Some illustrative examples for applications of [Formula: see text]-Tangent operators are also presented.

On the unified family of generalized Apostol-type polynomials of higher order and multiple power sums

In last last decade, many mathematicians studied the unification of the Bernoulli and Euler polynomials. Firstly Karande B. K. and Thakare N. K. in [6] introduced and generalized the multiplication formula. Ozden et. al. in [14] defined the unified Apostol-Bernoulli, Euler and Genocchi polynomials and proved some relations. M. A. Ozarslan in [13] proved the explicit relations, symmetry identities and multiplication formula. El-Desouky et. al. in ([3], [4]) defined a new unified family of the generalized Apostol-Euler, Apostol-Bernoulli and Apostol-Genocchi polynomials and gave some relations for the unification of multiparameter Apostol-type polynomials and numbers. In this study, we give some symmetry identities and recurrence relations for the unified Apostol-type polynomials related to multiple alternating sums.

On Barnes beta distributions, Selberg integral and Riemann xi

The theory of Barnes beta probability distributions is advanced and related to the Riemann xi function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma functions are reviewed using the approach of Ruijsenaars and shown to imply novel properties of Barnes beta distributions. The applications are given to the meromorphic extension of the Selberg integral as a function of its dimension and the scaling invariance of the underlying probability distribution. This probability distribution in the critical case is described and conjectured to be the distribution of the derivative martingale. The Jacobi triple product is interpreted probabilistically resulting in an approximation of the Riemann xi function by the Mellin transform of the logarithm of a limit of Barnes beta distributions.