MATH 60 Fall 2014 Midterm 1 Study Guide Topics

MATH 60 Fall 2014 Midterm 1 Study Guide Topics - Math 60...

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Math 60. Rumbos Fall 2014 1 Topics for Exam 1 1. Vector Space Structure in Euclidean Space 1.1 Definition of n –Dimensional Euclidean Space 1.2 Vector addition and scalar multiplication 1.3 Spans 1.4 Linear independence 2. Subspaces of Euclidean Space 2.1 Bases 2.2 Dimension 2.3 Coordinates 3. Connections with the Theory of Linear Equations 3.1 Homogeneous systems 3.2 Fundamental Theorem for homogenous systems of linear equations 3.3 Nonhomogeneous systems Relevant sections in text : 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6. Relevant sections in the online class notes : 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10 and 2.11. Relevant assignments : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.
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Unformatted text preview: Important concepts : Euclidean space, linear independence, span, subspaces, bases, dimension and coordinates. Important skills : Know how to determine whether subsets of R n are linearly in-dependent; know how to tell whether a given subset of R n is a subspace; know how to tell whether a set of vectors in R n spans a subspace; know how to compute the span of a set of vectors; know how to solve systems of linear equations; know how to determine bases for subspaces of Euclidean space; know how to compute dimensions of subspaces; know how to ﬁnd coordinates of vectors relative to ordered bases....
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