By Robert A Beezer

A primary path in Linear Algebra is an advent to the fundamental strategies of linear algebra, in addition to an advent to the strategies of formal arithmetic. It starts off with structures of equations and matrix algebra ahead of getting into the speculation of summary vector areas, eigenvalues, linear modifications and matrix representations. It has a variety of labored examples and routines, in addition to targeted statements of definitions and whole proofs of each theorem, making it excellent for self reliant learn.

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**Sample text**

It is just a number, but is a convenient way to talk about the individual entries simultaneously. This notation will get a heavy workout once we get to Chapter M. Example AM A matrix B= −1 1 −4 2 5 0 −6 2 2 3 1 −2 is a matrix with m = 3 rows and n = 4 columns. We can say that [B]2,3 = −6 while [B]3,4 = −2. When we do equation operations on system of equations, the names of the variables really are not very important. Use x1 , x2 , x3 , or a, b, c, or x, y, z, it really doesn’t matter. In this subsection we will describe some notation that will make it easier to describe linear systems, solve the systems and describe the solution sets.

9 0 −3 Definition AM Augmented Matrix Suppose we have a system of m equations in n variables, with coefficient matrix A and vector of constants b. Then the augmented matrix of the system of equations is the m × (n + 1) matrix whose first n columns are the columns of A and whose last column (n + 1) is the column vector b. This matrix will be written as [ A | b]. The augmented matrix represents all the important information in the system of equations, since the names of the variables have been ignored, and the only connection with the variables is the location of their coefficients in the matrix.

It is just a number, but is a convenient way to talk about the individual entries simultaneously. This notation will get a heavy workout once we get to Chapter M. Example AM A matrix B= −1 1 −4 2 5 0 −6 2 2 3 1 −2 is a matrix with m = 3 rows and n = 4 columns. We can say that [B]2,3 = −6 while [B]3,4 = −2. When we do equation operations on system of equations, the names of the variables really are not very important. Use x1 , x2 , x3 , or a, b, c, or x, y, z, it really doesn’t matter. In this subsection we will describe some notation that will make it easier to describe linear systems, solve the systems and describe the solution sets.