2.4 Gaussian Elimination and Pivoting
2.4 Gaussian Elimination and Pivoting
Theorem 3. 7.(Elementary Transformations). The following opera- tions applied to a linear system yield an equivalent system: (1) Interchange: The order of two equations can be changed (2)Scaling Multiplying an equation by a nonzero constant (3)Replacement: An equation can be replaced by the sum of itself and a nonzero multiple of any other equation
Example 3. 15. Find the parabola y=A+Bc+Ca- that passes througl the three points(1, 1),(2,-1), and(3,1)
A+B+C=1 at(1, A+2B+4C=-1at(2,-1) 215) A+3B+9C=1at(3,1)
A+B+C 芦+3C=2 26+0=0
A+B+C= 1 芦+C=2
2.5 Trianqular Factorization
2.5 Triangular Factorization
121314 111213214 21022a23a14 22023 4 031a32033a34 m11m732 000 u33134 4142a43a44 m41m742m043 0044
4.5. 1 Solution of a linear syste
4.5.1 Solution of a linear System
4.5.2 Triangular factorization
4.5.2 Triangular Factorization
