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DrDelMath

College Algebra
by Blitzer
SUMMARY

 

 

Chapter 6:  Matrices and Determinants

Section 6.1: Matrices Solutions to Linear Systems

Some additional links

1. Summary of elementary matrix theory
2. More about matrices
3. Elementary Row Operations
4. Elementary Row Operations Calculator

Example:


When it is desirable to emphasize the notation used for individual entries we use [aij] instead of capital A to name the matrix.

Example:

Example:
Consider the following system of equations:


The corresponding coefficient matrix is:


and the augmented matrix is:

Example:

Elementary Row Operations:
1. Interchange two rows
2. Multiply a row by a non-zero constant and replace that row with the product.
3. Add a multiple of a row to another row and replace one but not both of the rows with that sum.

DEFINITION: Two matrices are row equivalent if one can be obtained from the other by a sequence of elementary row operations.

Section 6.2: Inconsistent and Dependent Systems

Section 6.3: Matrix Operations

Here are some additional links.

3. Matrix Multiplication
4. Matrix multiplication calculator

Show Example Show Example

 

Show Example Show Example Show Example

 

Sample Exercises

The sample exercises referenced above are interactive. Instruction and learning depends on the reader pointing to items on the page to create pop-up explanations.

Minimal List of Exercises Page 588.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 6.3 Exercise Set: All exercises 1 - 36.

Section 6.4: Multiplicative Inverses of Matrices and Matrix Equations

Information about finding the inverse of a square matrix is found in the PDF file HERE.

Here are some links to additional websites about Matrix INVERSION.

1. Old Dominion University -- Linear Algebra Calculators for Learning
2. Basic Lesson for Matrix Inversion
3. Finding the Inverse of a Matrix
4. Finding the inverse of a Matrix

Minimal List of Exercises Page 603.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 6.4 Exercise Set: 1 - 12, 15, 17, 19, 21, 2529, 30, 31, 32, 37, 39, 40.

Section 6.5: The Determinant of a Square Matrix

Show Example Show Example Show Example Show Row 1 Cofactor Expansion
Show Row 2 Cofactor Expansion
Show Row 3 Cofactor Expansion

Minimal List of Exercises Page 616.

If you understand the previous material you should be able to answer the following questions.
Each of these questions should be answered. Most of these questions are included in the MyMathLab homework requirement. If a particular concept is difficult for you, you should study the related text material and then try to answer some additional questions from the list provided by the department. In each case you are expected to make an honest adult evaluation of your understanding of the concept. Your ability to answer these questions is one tool to help you make that evaluation.
Section 6.5 Exercise Set: All of 1 - 10, 27 - 32, 41, 42, 44, 49, 50.