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September 21st, 2017, 11:53 AM  #1 
Newbie Joined: Sep 2017 From: Canada Posts: 2 Thanks: 0  Problems about linear combination, direction numbers, and transposes
Hello everyone, I have some math homework here I can't quite understand: Q3: (a) Express the given vector as a linear combination of base vectors: (b) Find the direction numbers and direction cosines of each vector. c) Find the transpose of each vector. i) v = [2] [5]. ii) v = [2] [2] [3] How would I go about solving these 3 questions? A simple step solution is enough. Don't need to go into too much detail. Thanks! 
September 21st, 2017, 01:22 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond 
Aside from (b), I can say these questions are not difficult. What have you tried? Do you need to find out definitions of the terms used in the questions? As for (b), I'm not familiar with "direction numbers" 
September 21st, 2017, 01:22 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 669 
You need to clarify the question. (a,b,c) all refer to vectors (given, base, each). What are the vectors?

September 21st, 2017, 03:44 PM  #4 
Newbie Joined: Sep 2017 From: Canada Posts: 2 Thanks: 0 
I mainly need help on subquestion b. The vectors are [2, 5] for i and [2, 2, 3] for ii. So find the direction vectors and direction cosines for vector [2, 5] as well as [2, 2, 3] 
September 21st, 2017, 05:15 PM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1122 Math Focus: Elementary mathematics and beyond 
This page will help. It explains a method for calculating direction cosines in threespace as well as some general information. I suggest you take a look, if you're willing.

September 22nd, 2017, 04:06 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
Problem (a) says "Express the given vector as a linear combination of base (basis) vectors". What basis vectors? Any vector space has an infinite number of bases. Do you mean the standard basis vectors for $\displaystyle R^2$ and $\displaystyle R^3$? "Direction cosines" of a vector are the cosines of the angles the vector makes with the coordinate axes. They are also the components of a unit vector in the same direction. The "direction numbers" are the direction cosines multiplied a factor to give the correct length to the vector. They are also the components of the vector. 

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combination, direction, linear, numbers, problems, transposes 
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