Abstract
The linear transformation is a function relating the vector ke . If , then the transformation is called a linear operator. Several examples of linear operators have been introduced since SMA such as reflexive, rotation, compression and expansion and shear. Apart from being introduced in SMA, these linear operators were also introduced to the linear algebra course. Linear transformations studied at the university level include linear transformation in finite dimension vector spaces . The discussion includes how to determine the standard matrix for reflexive linear transformations, rotation, compression and expansion and given shear. Through the column vectors of reflexive, rotation, compression and expansion and shear, a standard matrix of 2x2 size is formed for the corresponding linear transformation. however, in this study, the authors studied linear transformations in dimensioned vector spaces . The results of this study are if known is a vector space with finite and the standard matrix for reflexivity, rotation, expansion, compression and shear is obtained. Each of these linear transformations is performed on x-axis, y-axis and z-axis on to get column vectors. The column vectors as a result of the linear transformation at form the standard matrix for the corresponding linear transformation in the vector space. The standard matrix for linear transformations in the vector space is obtained by determining reflexivity, rotation, expansion, compression and shear. The process of obtaining a standard matrix for linear transformation is carried out by rewriting the standard basis, determining the column vectors, and rearranging them as the standard matrix for each linear transformation in the vector space
Highlights
The transformation is called a linear operator
The discussion includes how to determine the standard matrix for reflexive linear transformations, rotation, compression and expansion and given shear
Through the column vectors of reflexive, rotation, compression and expansion and shear, a standard matrix of 2x2 size is formed for the corresponding linear transformation. in this study, the authors studied linear transformations in dimensioned vector spaces
Summary
Beberapa contoh operator linier telah diperkenalkan sejak. SMA seperti refleksif, rotasi, kompresi dan ekspansi serta geseran. Selain diperkenalkan di SMA, operatoroperator linier ini juga diperkenalkan pada mata kuliah aljabar linier. . Pembahasan meliputi bagaimana menentukan matriks baku untuk transformasi linier refleksif, rotasi, kompresi dan ekspansi serta geseran yang diberikan. Melalui vektor - vektor kolom dari refleksif, rotasi, kompresi dan ekspansi serta geseran dibentuk matriks baku-matriks baku berukuran 2x2 untuk transformasi linier yang bersesuaian. Namun pada penelitian ini, penulis mengkaji transformasi linier pada ruang vektor berdimesi. METODE PENELITIAN Metode yang digunakan pada penelitian ini adalah vektor-vektor kolom sebagai hasil transformasi linier pada ruang vektor.
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