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 nnumbers, it is called a n-dimensional vector. So the vector Agiven by =naaaA21is a n-dimensional column vector with ncomponents, naaa,......,,21. The above is a column vector. A row vector ][Bis of the form ],....,,[21nbbbB=where Bis a n-dimensional row vector with ncomponents nbbb,....,,21. Example 1 Give an example of a 3-dimensional column vector. Solution Assume a point in space is given by its ),,(zyxcoordinates. Then if the value of 5,2,3===zyx, the column vector corresponding to the location of the points is =523zyx.
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