This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MA 265 LECTURE NOTES: FRIDAY, JANUARY 11 Matrices (contd) Review of Definitions. Recall that the coefficients in a system of m linear equation in n unknowns a 11 x 1 + a 12 x 2 + + a 1 n x n = b 1 a 21 x 1 + a 22 x 2 + + a 2 n x n = b 2 . . . . . . . . . . . . a m 1 x 1 + a m 2 x 2 + + a mn x n = b m correspond to an m n matrix: A = a 11 a 12 . . . a 1 n a 21 a 22 . . . a 2 n . . . . . . . . . . . . a m 1 a m 2 . . . a mn . Examples. Consider the following two matrices: A = bracketleftbigg 1 2 3 1 1 bracketrightbigg and B = bracketleftbigg 1 + i 4 i 2 3 i 3 bracketrightbigg . Since A 2 rows and 3 columns, it is a 2 3 matrix. Since B has 2 rows and 2 columns, it is a 2 2 matrix. Note that the entries can either be real or complex numbers. Matrix Operations Matrix Addition. Say that A and B are both m n matrices. Then we define the addition as the m n matrix A = bracketleftbig a ij bracketrightbig , B = bracketleftbig b ij bracketrightbig = A + B = bracketleftbig a ij + b ij bracketrightbig . Note that addition can only be defined when A and B have both the same number of rows m and the same number of columns n . Example. Consider the following 2 3 matrices: A = bracketleftbigg 1 2 3 2 1 4 bracketrightbigg and B = bracketleftbigg 2 1 1 3 4 bracketrightbigg...
View
Full
Document
This note was uploaded on 02/25/2010 for the course MA 00265 taught by Professor ... during the Spring '10 term at Purdue University Calumet.
 Spring '10
 ...

Click to edit the document details