Overview of Week 7
Math 208 Section A, November 8, 2021
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Reading Assignment:
- Sections 4.1 and 4.2, Due Friday 11/05/21
- Sections 4.3 and 4.4, Due Friday 11/12/21
- Section 5.1, Due Monday, 11/15/21
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- Section 4.2, due 11/03/21
- Section 4.3, due 11/08/21
- Section 4.4, due 11/10/21
- Section 5.1, due 11/15/21
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Conceptual Problems:
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Vocabulary List:
- Chapter 4:
- Subspace
- The range and null space of a matrix as subspace.
- the range and kernel of a linear transformation as subspaces.
- How to obtain the matrix associated with a linear transformation.
- The Unifying Theorem: Versions 4, 5, and 6
- A basis for a subspace.
- The dimension of a subspace.
- The row space of a matrix.
- The column space of a matrix.
- The rank and nullity of a matrix.
- The Rank Plus Nullity Theorem.
- Coordinate vectors with respect to a given basis.
- The standard basis.
- Change of basis matrices, and change of basis formulas.
- Change of basis in a subspace.
- Chapter 5:
- The determinant, Definition 5.4
- cofactors and the cofactor expansion of the determinant
- Unifying Theorem: Version 7
- properties of the determinant: Theorems 5.8, 5.9, 5.10, 5.11, 5.12, 5.13, 5.15, 5.16
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Key Concepts:
- Chapter 4
- subspaces and vectors that span them
- basis and dimension of a subspaces
- range and null space of a matrix
- range and kernel of linear transformation
- row and column space of a matrix
- rank and nullity of a matrix and the Rank Plus Nullity Theorem
- change of bases
- Chapter 5
- the determinant and all of its properties
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Skills to Master:
- Chapter 4
- Checking to see if a set of vectors is a subspace.
- Computing bases for the range and null space of a matrix.
- Computing bases for the range and kernel of a linear transformation.
- Computing a basis for a subspace and determining it dimension.
- Computing bases for the row and column spaces of a matrix.
- Computing the dimensions of the row and column spaces of a matrix.
- Computing the rank and nullity of a matrix.
- Applying the Rank Plus Nullity Theorem.
- Computing a change of basis matrix.
- Chapter 5
- Computing determinants by using the properties of the determinant