Matrix Algebra - If A and B are both m n matrices then the...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: If A and B are both m n matrices then the sum of A and B , denoted A + B , is a matrix obtained by adding corresponding elements of A and B . -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B - = + 2 B A If A and B are both m n matrices then the sum of A and B , denoted A + B , is a matrix obtained by adding corresponding elements of A and B . add these -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B -- = + 2 2 B A add these -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B -- = + 6 2 2 B A add these -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B -- = + 2 6 2 2 B A add these -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B -- = + 2 6 2 2 B A add these -- = 3 1 2 2 1 A -- = 4 1 2 4 3 B --- = + 1 2 6 2 2 B A add these A B B A + = + C B A C B A + + = + + ) ( ) ( If A is an m n matrix and s is a scalar, then we let kA denote the matrix obtained by multiplying every element of A by k. This procedure is called scalar multiplication. ( 29 ( 29 ( 29 ( 29 k hA kh A k h A kA hA k A B kA kB = + = + + = + -- = 3 1 2 2 1 A ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 -- = -- = 9 3 6 6 3 3 3 1 3 3 2 3 2 3 1 3 3 A PROPERTIES OF SCALAR MULTIPLICATION The m n zero matrix , denoted , is the m n matrix whose elements are all zeros. ( 29 ) ( = =- + = + A A A A A [ ] 2 2 1 3 The multiplication of matrices is easier shown than put into words. You multiply the rows of the first matrix with the columns of the second adding products -- = 1 4 1 2 3 A -- = 1 3 3 1 4 2 B Find AB First we multiply across the first row and down the...
View Full Document

This note was uploaded on 01/12/2011 for the course MAT 116 A MAT 116 A taught by Professor Hawkins during the Spring '10 term at University of Phoenix.

Page1 / 19

Matrix Algebra - If A and B are both m n matrices then the...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online