MA 253 Reading Assignemtns

Homework problems are on a separate webpage. Reading assignments must be done by the class period after they are assigned.

Date Assigned Reading What to focus on:

Wed.
Sept. 3 Section 1.1

The mechanics of solving systems of equations
The geometric interpretation of solving systems of linear equations
The number of possible solutions to a system of linear equations

Fri.
Sept. 5 Section 1.2

What are legal row operations?
How is a system of linear equations converted to a matrix?
What is reduced row-echelon form?

Mon.
Sept. 8 Section 1.3

How do you find the rank of a matrix?
What is the relationship between the numbers of variables and equations in a linear system and the number of possible solutions?
How do you add and multiply matrices?
What is a linear combination of vectors?

Fri.
Sept. 12 Section 2.1

How does Def. 2.1.1 differ from the one given in class?
Pay attention to Example 9!
Pay attention to Def. 2.1.4

Mon.
Sept. 15 Section 2.2

Work through Example 1 carefully
Understand Def. 2.2.1
Memorize Theorem 2.2.3

Mon.
Sept. 17 Section 2.3

Most of this we've covered already, just look over the section.

Mon.
Sept. 21 Section 2.4

How can we calculate the inverse of a matrix?
Why does the method work?

Wed.
Sept. 24 Section 3.1

What is the kernel of a linear transformation?
What is the image of a linear transformation?
How do we calculate the kernel and image?
What does it mean to say that the kernel and image are subspaces?

Fri.
Oct. 3 Section 3.2

What does it mean for vectors to be linearly independent?
How can you eliminate redundant vectors from a list?

Mon
Oct. 6 Section 3.3

How can we tell if a set of spanning vectors for a subspace is a basis?
How do we prove that all bases for a subspace have the same number of elements?
How do we show that every vector in a subspace has a unique representation with respect to a given basis?

Wed
Oct. 8 Section 3.4

Given a basis, how do we represent vectors with respect to that basis?
Given a basis and a linear transformation how do we find a matrix for that linear transformation with respect to the basis?

Wed
Oct. 15 Sections 6.1 - 6.2

What are two different ways of calculating the determinant?
Why is that a linear transformation is invertible if and only if its determinant is 0?
Also remember the additional reading assignment passed out in class.

Mon
Oct. 20 Sections 7.1

What is an eigenvalue and an eigenvector?
How do we calculate them?

Mon
Oct. 20 Sections 7.2, 7.3, 7.5

Why do similar matrices have the same eigenvalues?
What are algebraic and geometric multiplicity?
What is the relationship between transition matrices and eigenvectors?
What is the significance of complex eigenvalues?

Wed.
Oct. 29 Sections 5.1, 5.3

What does it mean for vectors to be orthonormal?
What is an orthogonal complement of a subspace? Does every subspace have one?
What is a correlation coefficient? What is its relationship to dot product?
What is an orthogonal matrix? What are the properties of an orthogonal transformation?
How do we find the matrix of an orthogonal projection onto a subspace? Why does the method work?

Date Assigned	Reading	What to focus on:
Wed. Sept. 3	Section 1.1	The mechanics of solving systems of equations The geometric interpretation of solving systems of linear equations The number of possible solutions to a system of linear equations
Fri. Sept. 5	Section 1.2	What are legal row operations? How is a system of linear equations converted to a matrix? What is reduced row-echelon form?
Mon. Sept. 8	Section 1.3	How do you find the rank of a matrix? What is the relationship between the numbers of variables and equations in a linear system and the number of possible solutions? How do you add and multiply matrices? What is a linear combination of vectors?
Fri. Sept. 12	Section 2.1	How does Def. 2.1.1 differ from the one given in class? Pay attention to Example 9! Pay attention to Def. 2.1.4
Mon. Sept. 15	Section 2.2	Work through Example 1 carefully Understand Def. 2.2.1 Memorize Theorem 2.2.3
Mon. Sept. 17	Section 2.3	Most of this we've covered already, just look over the section.
Mon. Sept. 21	Section 2.4	How can we calculate the inverse of a matrix? Why does the method work?
Wed. Sept. 24	Section 3.1	What is the kernel of a linear transformation? What is the image of a linear transformation? How do we calculate the kernel and image? What does it mean to say that the kernel and image are subspaces?
Fri. Oct. 3	Section 3.2	What does it mean for vectors to be linearly independent? How can you eliminate redundant vectors from a list?
Mon Oct. 6	Section 3.3	How can we tell if a set of spanning vectors for a subspace is a basis? How do we prove that all bases for a subspace have the same number of elements? How do we show that every vector in a subspace has a unique representation with respect to a given basis?
Wed Oct. 8	Section 3.4	Given a basis, how do we represent vectors with respect to that basis? Given a basis and a linear transformation how do we find a matrix for that linear transformation with respect to the basis?
Wed Oct. 15	Sections 6.1 - 6.2	What are two different ways of calculating the determinant? Why is that a linear transformation is invertible if and only if its determinant is 0? Also remember the additional reading assignment passed out in class.
Mon Oct. 20	Sections 7.1	What is an eigenvalue and an eigenvector? How do we calculate them?
Mon Oct. 20	Sections 7.2, 7.3, 7.5	Why do similar matrices have the same eigenvalues? What are algebraic and geometric multiplicity? What is the relationship between transition matrices and eigenvectors? What is the significance of complex eigenvalues?
Wed. Oct. 29	Sections 5.1, 5.3	What does it mean for vectors to be orthonormal? What is an orthogonal complement of a subspace? Does every subspace have one? What is a correlation coefficient? What is its relationship to dot product? What is an orthogonal matrix? What are the properties of an orthogonal transformation? How do we find the matrix of an orthogonal projection onto a subspace? Why does the method work?