mws_gen_sle_bck_vectors - Chapter 04.02 Vectors After...

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04.02.1 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 = 5 2 3 z y x .
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