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Chapter 2 Euclidean Vectors (EV)
Learning Outcomes
What is a space of Euclidean vectors?
By the end of this chapter, you should be able to...
Determine if a Euclidean vector can be written as a linear combination of a given set of Euclidean vectors by solving an appropriate vector equation.
Determine if a set of Euclidean vectors spans \(\IR^n\) by solving appropriate vector equations.
Determine if a subset of \(\IR^n\) is a subspace or not.
Determine if a set of Euclidean vectors is linearly dependent or independent by solving an appropriate vector equation.
Explain why a set of Euclidean vectors is or is not a basis of \(\IR^n\text{.}\)
Compute a basis for the subspace spanned by a given set of Euclidean vectors, and determine the dimension of the subspace.
Find a basis for the solution set of a homogeneous system of equations.
Readiness Assurance.
Before beginning this chapter, you should be able to...
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Use set builder notation to describe sets of vectors.
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Add Euclidean vectors and multiply Euclidean vectors by scalars.
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Perform basic manipulations of augmented matrices and linear systems.
www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/adding-vectors
www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/multiplying-vector-by-scalar
