Vector Spaces, Basis and Closest Vector
Not what you're looking for?
1. Let S be a subset of R described as follows:
S {(x,y,z) :x+y+z = 0}
(a) Show that S is a vector space.
(b) Calculate a basis of S and compute it dimension.
(c) Find the vector in S which is closest to the vector (1,3, ?5) in R3.
Purchase this Solution
Solution Summary
Vector Spaces, Basis and Closest Vector are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
Solution Preview
Proof:
(a) For any u=(x,y,z),v=(x',y',z') in S, we have
x+y+z=x'+y'+z'=0
Then u+v=(x+x',y+y',z+z') and we have
(x+x')+(y+y')+(z+z')=(x+y+z)+(x'+y'+z')=0+0=0
For any real number c, we have
...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts