Matrices and Vectors

This applet demonstrates how vector multiplication and vector addition are related to matrix addition and matrix multiplication. Move the red and white vectors around and watch what happens to the light blue matrix and light green matrix. Observe how the light blue vector and light green vector correspond to the changes in the light blue matrix and light green matrix.

Objectives that this applet covers:

 Students will be able to perform the basic operations on vectors and matrices (Algorithmic Skill)

 Students will be able to explain the connection between matrix operations and vector operations. (Comprehension and Communication)

Some interesting questions to consider:

 What happens when the white vector is multiplied by the red vector when the red vector is the identity matrix?

 What happens when the ones are replaced with two other equivalent values?

 What is the relationship between the dot product of two vectors and vector multiplication?

 What is the relationship between vector addition and matrix addition?



Note that this applet corresponds to the following standards of the new Common Core Curriculum that can be found at the website Common Core Standard Initiative that was published in 2012. The website’s URL is http://www.corestandards.org/Math. Once there, go to High School: Number and Quantity—Vector and Matrix Quantities:

 CCSS.Math.Content.HSN-VM.C.8

 CCSS.Math.Content.HSN-VM.B.5a.

 CCSS.Math.Content.HSN-VM.C.7

 CCSS.Math.Content.HSN-VM.C.10

 CCSS.Math.Content.HSN-VM.C.11

Jeremy Hidalgo, Created with GeoGebra