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Math 20F. Final Exam December 7, 2005
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for un
Print Name: Math 20F. Midterm Exam 1 October 17, 2005
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported
Math 20F Linear Algebra
Lecture 1
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A primer on Linear Algebra
Slide 1
Remarks on the course.
Overview of Linear Algebra.
Systems of linear equations.
(Row approach) (Sec. 1.1).
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Linear
Math 20F Linear Algebra
Lecture 4
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A matrix is a function
Slide 1
Review: Column picture.
Matrix equation Ax = b.
A matrix is a linear function.
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The column picture is essential for lin
Math 20F Linear Algebra
Lecture 12
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Change of basis
Slide 1
Review: Components of a vector in a basis.
Change of basis.
Review: Midterm 1.
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Any vector can be decomposed in an unique way
Math 20F Linear Algebra
Lecture 15
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Linear Transformations
Domain, range, and null spaces.
Slide 1
Injective and surjective transformations.
Bijections and the inverse.
Nullity + Rank Theorem
Math 20F Linear Algebra
Lecture 18
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Determinants, n n
Review: The 3 3 case.
Slide 1
Determinants n n.
(Expansions by rows and columns.
Relation with Gauss elimination matrices: Properties.)
Fo
Math 20F Linear Algebra
Lecture 6
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Matrix operations
Review:
Slide 1
Linear combinations of matrices.
Multiplication of matrices.
Gauss elimination using matrix multiplication.
Inverse matri
Math 20F Linear Algebra
Lecture 9
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The beginning of Linear Algebra
Review
Slide 1
Broad overview.
Main results (so far).
Examples.
The need of abstraction: Vector Space.
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Main results
Math 20F Linear Algebra
Lecture 20
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On determinants and eigenvalues
Slide 1
Review: eigenvalues and eigenvectors.
Eigenspaces.
Characteristic equation.
Multiplicity of eigenvalues.
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Th
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Math 20F. Midterm Exam 2 November 21, 2005
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given f