VM - Using Vectors and Matrices to Make Decisions Overview

Using Vectors and Matrices to Make Decisions Overview

In this Module, we will discover Vectors and Matrices. You may have heard of them before in Physics, but the big idea will be to understand how two forces work on object. You will utilize right triangle trigonometry as well as Unit Circle trigonometry. Matrices can be used to display and organize data. When data is organized in a matrix, you can add, subtract and even multiply the data to manipulate it! You will come to see that matrices have many of the same properties as real numbers, except when multiplied! Not only can you display data with matrices, you can also solve systems of equations and transform geometric figures.

Essential Questions

How can I use vector operations to model, solve and interpret real-world problems?
How are vector and scalar quantities similar and different?
How can I represent addition, subtraction, and scalar multiplication geometrically?
What are different ways to geometrically represent the addition of vectors?
In what ways can matrices transform vectors?
How can we represent data in matrix form?
How do you work with matrices as transformations in the plane?

Key Terms

The following key terms will help you understand the content in this module

Components of a Vector – a and b in the vector〈a,b〉. The horizontal component is a and the vertical component is b.
Force - The push or pull on an object
Force vector - a representation of a force that has both magnitude and direction
Dimensions of a Matrix - the number of rows by the number of columns
Initial Point – The point at the tail of the arrow representing a vector. The initial point is the origin if the vector is in standard position.
Magnitude of a Vector – The distance between vector's initial and terminal points denoted ‖v‖, | $LaTeX: \overline{v}$ $\overline{v}$ |, or |v|. $LaTeX: \lVert{v}\rVert = \lVert{a, b}\rVert =\sqrt{a^2 +b^2}$ $\lVert{v}\rVert = \lVert{a, b}\rVert =\sqrt{a^2 +b^2}$ .
Matrix - a rectangular array of numbers displayed in row and columns that can be manipulated according to a set of rules.
Resultant Vector – The vector that results from adding two or more vectors.
Scalar – A real number. A scalar has a magnitude but not direction.
Terminal Point – The point at the "tip" of the arrow representing a vector.
Vector – A mathematical object that has both magnitude and direction, expressed as v, $LaTeX: \overline{v}$ $\overline{v}$ , or〈a,b〉or as a directed line segment.