Lesson 2 … and Row by Column Solidify Understanding
Jump Start
Multiply the two matrices together to find the product matrix:
Learning Focus
Use matrix multiplication in context.
How do I use matrix multiplication to model contexts that depend on summing up multiple partial products?
Open Up the Math: Launch, Explore, Discuss
In the previous lesson, you chose a context and wrote a story for the information given in the following augmented matrix:
Your story could also have been represented by the following system of equations:
1.
Use the following to review how matrix multiplication works.
a.
Explain how this matrix equation given represents the system of equations previously given.
b.
Now verify that
2.
In a context, each entry in a matrix represents two pieces of information, depending on the row and column in which it is located. Organize the following information into a matrix, and label the rows and columns.
Week 1: Clarita painted
curbside logos and Carlos painted driveway mascots. Week 2: Clarita painted
curbside logos and Carlos painted driveway mascots. Week 3: Clarita painted
curbside logos and Carlos painted driveway mascots.
3.
Carlos and Clarita charge
Ready for More?
A photographer sells framed photos in
During the weeks prior to Mother’s Day the photographer uses
Assembling the framed photos includes cutting the paper at
Use this information to find the total cost and assembly time for each holiday using matrix multiplication.
Takeaways
Matrices can be multiplied together if their dimensions are compatible. This means:
For example, these two matrices can be multiplied together:
When used to model a context, matrices can be multiplied together if their units are compatible. This means:
Using the matrices given above, describe and illustrate how to find the matrix product
Lesson Summary
In this lesson, we reviewed the row-by-column procedure for multiplying matrices, and used matrix multiplication to model a context.
1.
Add the matrices.
2.
Create two matrices that cannot be added.
3.
What is the meaning of
4.
What is the meaning of