MATH 2601: WEEK 3

Topics for this week are:

• Application of Gaussian elimination
• review of linear transformations in plane and space
• Vectorspaces, coordinates, bases
• Matrices of general linear maps

Text coverage:

    Sub-sections 4.4-4.6 from Section 4 of the [Notes:Th], Sub-sections 5.1-5.4 from Section 5 of the [Notes:Th].

Linear transformations (concise version of Ch. 4 of [Demko])

Online resources:

• Online notes
  • [Notes:Th] Section 4 Using Gaussian elimination: Column space, nullspace, rank, nullity, linear independence, inverse matrix
  • [Notes:Th] Section 5 Vectorspace, coordinates with respect to a basis. Change os basis. Linear functions and their matrices
• Answers to selected problems

Assignment for this week:

• Problems:
  • Problems on linear transformations at the end of Linear transformations (concise version of Ch. 4 of [Demko])
  • Additional problems (Problem set #3)
• Challenge Problem: Prove that the vectorspace of continuous functions on [0,1] cannot be spanned by finitely many elements (hence it is not finite dimensional). [Hint: Prove by contradiction. If there is a spanning set of n elements, consider n+1 distinct points in [0,1]. Show that the linear combinations of the spanning set cannot take on arbitrary values at these n+1 points, while a general continuous function can.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.