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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...
Use set builder notation to describe sets of vectors.
Add Euclidean vectors and multiply Euclidean vectors by scalars.
Perform basic manipulations of augmented matrices and linear systems.
