Chapter 3. Matrices
Chapter 3. MatricesThis material is in Chapter 1 of Anton & Basic matrix notationWe recall that amatrixis a rectangular array or table of numbers. We call the individual numbersentriesof the matrix and refer to them by their row and column numbers. The rows are numbered1,2, . . .from the top and the columns are numbered1,2, . . .from left to we use what you might think of as a(row, colum)coordinate system for the entries of a the example 1 1 2 51 11 13 22 1 3 4 13 is the(2,3)entry, the entry in row 2 and column matrix above is called a3 4matrix because it has 3 rows and 4 columns. We can talkabout Matrices of all different sizes such as[4 57 11]2 2[47]2 1[4 7]1 2 4 57 1113 13 3 2and in general we can havem nmatrices for anym 1andn with just one row are calledrow Matrices . A1 nmatrix[x1x2 xn]hasjust the same information in it as ann-tuple(x1, x2.)
Matrices with just one row are called row matrices. A 1 n matrix [ x 1 x 2 x n] has ... to identify 1 n matrices with n-tuples (which we know are points or vectors in Rn). We use the term column matrix for a matrix with just one column. Here is an n 1 (column) matrix 2 6 6 6 4 x 1 x 2... x n 3 7 7 7 5 and again it is tempting to think of these ...
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