UNDERSTANDING MATRICES

A WebQuest for Algebra II

by Elaine T. Cates

Introduction / Task / Resources / Process / Evaluation / Conclusion

Introduction

Many problems can be solved using a method sometimes referred to as matrix logic. You will create a table or matrix that helps you organize all the information in the problem. By using the matrix, you can eliminate one possibility after another until you eventually arrive at a solution.

You will learn that a matrix is a system of rows and columns and that each piece of data in the array has a purpose. You will learn the properties of matrices and how to name a matrix by its dimensions and use it to perform geometric translations and dilations. You will perform operations on matrices including addition, subtracation, and multiplication.

After completion of this unit, you will write the identity matrix for a 2x2 and a 3x3 matrix. You will find the inverse of a matrix and use it to solve a system of equations.

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TheTask

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Classroom Resources

Internet Resources

Logal Express

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The Process

  1. You will begin by providing real world examples of rows and columns and determine the differences. (A row contains your seat at a concert while columns can be found on the porches of many Southern homes.)
  2. Once you have a clear visual and mental understanding of rows and columns, you will try to provide uses for an array of values called a matrix.
  3. You will look at matrix examples, determine their dimensions, and name them using those dimensions.
  4. You will see how the commutative and associative properties of equality do or do not apply to matrices.
  5. Once you understand matrix dimensions and properties, you will then advance to the operations of addition, substraction, scalar multiplication, and finally, multiplication of one matrix by another a matrix.
  6. By using a coordinate matrix, you will perform dilations and translations on geometric figures.
  7. You will determine the identity matrix and inverse of a 2x2 and a 3x3 matrix.
  8. By using this inverse you will solve a system of equations in two and in three variables.
  9. Finally, you will solve problems involving practical situations by using matrices and inverse matrices.
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Evaluation

Each step in this process will be evaluated by a series of brief quizzes. The quizzes will be averaged together as a major test grade. At the conclusion of this project, your mastery of matrices will be determined by a major test.

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Conclusion

Now that you have had an opportunity to discover matrices and their properties, you can see the many uses for matrix logic in real world applications.

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