Transcription of Chapter 3. Matrices
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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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