# A first course in linear algebra, with concurrent examples by Alan G. Hamilton

By Alan G. Hamilton

This can be a brief, readable creation to easy linear algebra, as frequently encountered in a primary direction. the advance of the topic is built-in with a great number of labored examples that illustrate the information and strategies. The layout of the e-book, with textual content and appropriate examples on dealing with pages signifies that the reader can persist with the textual content uninterrupted. the coed might be capable of paintings in the course of the e-book and study from it sequentially. pressure is put on functions of the tools instead of on constructing a logical procedure of theorems. a number of routines are supplied.

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**Example text**

The number in the ith row and jth column is called the (i, j)-entry. ) may be used for the (i,j)-entry. The first suffix denotes the row and the second suffix the column. 1. A further notation which is sometimes used is [a;;] pxq. This denotes the p x q matrix whose (i,j)-entry is aij, for each i and j. Immediately we can see that there are extremes allowed under this definition, namely when either p or q is 1. When p is 1 the matrix has only one row, and is called a row vector, and when q is 1 the matrix has only one column, and is called a column vector.

Show the product AX has pth row consisting entirely of Os. Let A = [ai3]P x P, with aPj = 0 for I

E. the sum of all the products of the entries in the ith row of A with the respective entries in the jth column of B. Rule A p x q matrix can be multiplied on the right only by a matrix with q rows. IfAisapxgmatrix andBisagxrmatrix, then theproduct ABisapxr matrix. There is a useful mnemonic here. We can think of matrices as dominoes. A p, q domino can be laid next to a q, r domino, and the resulting `free' numbers are p and r. 9 illustrate the procedures in calculating products. It is important to notice that given matrices can be multiplied only if they have appropriate sizes, and that it may be possible to multiply matrices in one order but not in the reverse order.