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

By Alan G. Hamilton

It is a brief, readable creation to simple linear algebra, as often encountered in a primary direction. the advance of the topic is built-in with a lot of labored examples that illustrate the guidelines and strategies. The structure of the publication, with textual content and suitable examples on dealing with pages implies that the reader can stick with the textual content uninterrupted. the coed could be capable of paintings during the publication and study from it sequentially. pressure is put on purposes of the equipment instead of on constructing a logical procedure of theorems. quite a few workouts are supplied.

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Extra resources for A first course in linear algebra, with concurrent examples

Sample text

Which of the following matrices are symmetric, and which are skewsymmetric (and which are neither)? 1 [2 2 2 3]' [-2 3]' 1 0 2 L 2 ] 2 1 -1 1 2 0 [ -2 1 0 2 -3 2 J [3 3 3 0 1 0 _ 1]' [0 [3 -1 [ 0 1 [-22 01' -2 -011' 42 Exercises 0 0 [0 0J 1 [0 , -01 0 , -1 [1 1 7. Show that the following matrices are orthogonal. 1 -T - 2 - 5 5 2 1 4 3 T5 T5 5 5 2 1 1 1 1 11 1 0 4 3 7 T6 T3 1 G 7 7 8. Show that a product of two orthogonal matrices of the same size is an orthogonal matrix. 9. Describe in words the effect of premultiplying a 4 x 4 matrix by each of the elementary matrices below.

Evaluate the following matrix products. 2 '1 [35 4 (1) [2]. 3 2J 31 3. Matrices and algebraic vectors 0 1 (ii) 1 2 3 1 2 1 (iii) (iV) -1 -2 -1 3 -3 1 0 1 4 1 0 1 x 1 2 2 1 -1 -1 2 0 1 0 -3 -2 2 1 1 1 . 1 01 2 11 0l (3 41 -1 -1 0 41 . [ 0 1 1 2 -1 1 i I. 1 I 5. Obtain A3-2A2+A-I, when A= 1 1 2 1 1 1 2 1 1 6. How must the sizes of matrices A and B be related in order for both of the products AB and BA to exist? 1 Properties of a zero matrix. 2 ], f]-[0 e 01 0 Properties of an identity matrix. 3 01 0 a b 0[dg he b [dg h a b cl 1J-[g h kJ 1 a b cl 1 0 0 g h kJ [0 0 c e fk Examples of diagonal matrices.

An array of numbers with p rows and q columns is called a p x q matrix ('p by q matrix'), and the numbers themselves are called the entries in the matrix. 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.