ALJABAR LINEAR ELEMENTER – Ebook written by VERSI APLIKASI. Read this book using Google Play Books app on your PC, android, iOS devices. Sistem Informasi. Aljabar Linear Elementer Versi Aplikasi Jilid 2 Edisi 8. Share to: Facebook; Twitter; Google; Digg; Reddit; LinkedIn; StumbleUpon. Anton. Buy Aljabar Linear Elementer Versi Aplikasi Ed 8 Jl 1 in Bandung,Indonesia. Get great deals on Books & Stationery Chat to Buy.

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The set of all ordered n- tuples is called n-space and is denoted by Rn. Add a multiple of one row apliksi another row. If A is a square matrix, then the trace of A, denoted by tr Ais defined to be the sum of the entries on the main diagonal of A. Note A set S with two or more apliasi is: Multiply lnear equation through by a nonzero constant. To find the entry in row i and column j of ABsingle out row i from the matrix A and column j from the matrix B.

More generally, we define the determinant of an n x n matrix to be This method of evaluating det A is called cofactor expansion along the first row of A. Conversely, vectors with the same components are vefsi since they have the same length and the same direction. System of Linear Equations Howard Anton If A is any matrix and c is any scalar, then the product cA is the matrix obtained by linesr each entry of the matrix A by c. To be of reduced row-echelon form, a matrix must have the following properties: A matrix that has the first three properties is said to be in row-echelon form.

Jika terbukti melakukan kecurangan akademik berupa mencontek atau bekerja sama pada saat kuis, UTS dan UAS, maka akan mendapatkan sanksi nilai 0. Tidak berbincang-bincang selama proses belajar mengajar 5.


Each column that contains a leading 1 has zeros everywhere else in that column. Help Center Find new research papers in: Adjoin the identity matrix to the right side of A, thereby producing a matrix of the form [A I], apply row operations to this matrix until the left side is aljsbar to I; these operations will convert the right side to A-1, so the final matrix will have the form [I A-1]. Tidak meninggalkan sampah di ruangan kelas 6.

In addition, we shall regard the zero vector space to be finite dimensional. Essential Linear Algebra with Applications. If no such matrix B can be found, then A is said to be singular.

Multiply a row through by a nonzero constant.


Augmented Matrices A system of m linear equations in n unknowns can be abbreviated by writing only the rectangular array of numbers This is called the augmented matrix for the system. In any two successive rows that do not consist entirely of zeros, the leading 1 in the lower row occurs elemenger to the right than the leading 1 in the higher row.

In addition, we define the zero vector space to have dimension zero. This solution is called the trivial solution.

If, as shown in Figure 3. Let C be the “cost” matrix formed by the first set of data and let N be the matrix formed by the second set of data. If A is any m x n matrix, then elemente transpose of A, denoted by AT is defined to be the n x m matrix that results from interchanging the rows and columns of A ; that is, the first column of AT is the first row of A, the second column of AT is the second row of A, elementwr so forth.


Skip to main content. Toleransi Keterlambatan 15 Menit dari jadwal Perkuliahan 3. The matrix cA is said to be a scalar multiple of A. A matrix is a rectangular array of numbers. Method for Solving a System of Linear Equations Since the rows horizontal lines of an augmented matrix correspond to the equations in the associated system, these three operations correspond to the following operations on the rows of the augmented matrix: To see that T is linear, observe that: P Q R Material 1 2 1 Labor 3 2 2 Overheads 2 1 2 The numbers of items produced in one month at the four locations are as follows: To find the inverse of an invertible matrix A, we must find a sequence of elementary row operations that reduces A to the identity and then perform this same sequence of operations on In to obtain A Gaussian Elimination Howard Anton We shall call linear transformations from Rn to Rm matrix transformations, since they can be carried out by matrix multiplication.

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Remember me on this computer. Solution Consider a general system of two linear equations in the unknowns x and y: Two matrices are defined to be equal if they elemeenter the same size and their corresponding entries are equal. Vectors in Coordinate Systems If equivalent vectors, v and w, are located so that their initial points fall at the origin, then it is obvious that their terminal points must coincide since the vectors have the same length and direction ; thus the vectors have the same components.

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