1.2 Matrix Multiplication
In this section we look at various ways of viewing matrix multiplication. These different points of view are
useful to quickly see why certain formulas that arise later are valid.
If a = (a1, a2, , an) is a row vector and x = is
1.3 Implementing Matrix Operations in Programming Languages
1.3.1 General Principles
We saw in sections 1.1.2 and 1.1.3 how to solve a system of linear equations Ax = b in Mathematica and
MATLAB. Once the coefficient matrix A and the vector b on the right
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Solving Linear Equations
In this chapter we look at systems of linear equations, including applications and algorithms for their
solution. We begin by discussing applications of linear equations to approximating the solution of
differential equations.
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1.4 Gaussian Elimination Without Pivoting.
Gaussian elimination is one popular procedure to solve linear equations. As we shall see, it leads to a
decomposition of the coefficient matrix A as the product A = LU of a lower triangular matrix L and an upper