SOLUTIONS TO SIMULTANEOUS LINEAR ALGEBRAIC EQUATIONS Flashcards
A polynomial expression containing more than one variable, that has no exponent or power higher than 1.
LINEAR ALGEBRAIC EQUATIONS
The task here is to determine the values of x, y and z
System of linear algebraic equations
The number of unknowns must match the number of available equations as long as the system has a unique set of values for the variables (x, y and z).
System of linear algebraic equations
The solutions of ______ and ______ Equations make use of solutions to algebraic equations.
Mesh and Nodal
the common methods in solving systems of linear equations
A. ITERATIVE METHODS
B. MATRIX METHODS
A. ITERATIVE METHODS
A.1. Jacobi Iteration
A.2. Gauss-Seidel Iteration
B. MATRIX METHODS
B.1. Inverse Matrix
B.2. Gauss Elimination Method
B.3. Gauss-Jordan Elimination Method
B.4. LU Factorization
A matrix consists of a rectangular array (rows and columns) of elements represented by a single symbol.
Example: Matrix B is denoted by [B]
Matrix Notation
A matrix element is one of the quantities found inside a matrix. An element in Matrix B is denoted by bij, i and j gives the location of the element in the matrix –** i **for the **ith row **and **j **– for the jth column.
Example: b32 means that the element is in matrix B and found in the 3rd row and 2nd column
Matrix Element and Location
Matrix Size
m by n or m x n
Where
m: refers to the number of rows
n: refers to the number of columns
(3) Special Matrix
- square matrix
- column vector
- row vector
(6) Special Square Matrices
- Symmetric Matrix
- Diagonal Matrix
- Diagonally Dominant Matrix
- Identity Matrix
- Upper Triangular Matrix (U-Matrix)
- Lower Triangular Matrix (L-Matrix)
the elements in the ith row equals or matches the elements in the jth column.
Symmetric Matrix
the elements NOT found in the main diagonal are zero.
Diagonal Matrix
the ABSOLUTE value of the elements found in the main diagonal are the greatest value or magnitude in its row.
Diagonally Dominant Matrix
