mws_gen_sle_bck_vectors

# mws_gen_sle_bck_vectors - Chapter 04.02 Vectors After...

This preview shows pages 1–5. Sign up to view the full content.

Chapter 04.02 Vectors After reading this chapter, you should be able to: 1. define a vector, 2. add and subtract vectors, 3. find linear combinations of vectors and their relationship to a set of equations, 4. explain what it means to have a linearly independent set of vectors, and 5. find the rank of a set of vectors. What is a vector? A vector is a collection of numbers in a definite order. If it is a collection of n numbers, it is called a n -dimensional vector. So the vector A given by = n a a a A 2 1 is a n -dimensional column vector with n components, n a a a , ...... , , 2 1 . The above is a column vector. A row vector ] [ B is of the form ] , .... , , [ 2 1 n b b b B = where B is a n - dimensional row vector with n components n b b b , .... , , 2 1 . Example 1 Give an example of a 3-dimensional column vector. Solution Assume a point in space is given by its ) , , ( z y x coordinates. Then if the value of 5 , 2 , 3 = = = z y x , the column vector corresponding to the location of the points is 04.02.1

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

View Full Document
04.02.2 Chapter 04.02 = 5 2 3 z y x . When are two vectors equal? Two vectors A and B are equal if they are of the same dimension and if their corresponding components are equal. Given = n a a a A 2 1 and = n b b b B 2 1 then B A = if n i b a i i , ...... , 2 , 1 , = = . Example 2 What are the values of the unknown components in B if = 1 4 3 2 A and = 4 1 4 3 b b B and B A = . Solution 1 , 2 4 1 = = b b How do you add two vectors? Two vectors can be added only if they are of the same dimension and the addition is given by
Vectors 04.02.3 + = + n n b b b a a a B A 2 1 2 1 ] [ ] [ + + + = n n b a b a b a 2 2 1 1 Example 3 Add the two vectors = 1 4 3 2 A and - = 7 3 2 5 B Solution - + = + 7 3 2 5 1 4 3 2 B A + + - + = 7 1 3 4 2 3 5 2 = 8 7 1 7

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

View Full Document
04.02.4 Chapter 04.02 Example 4 A store sells three brands of tires: Tirestone, Michigan and Copper. In quarter 1, the sales are given by the column vector = 6 5 25 1 A where the rows represent the three brands of tires sold – Tirestone, Michigan and Copper respectively. In quarter 2, the sales are given by = 6 10 20 2 A What is the total sale of each brand of tire in the first half of the year?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern