# Mr. Germanis' Class Website

Unit Calendar (including Semester 1 final)
Unit Plan (including Vocabulary and CCSS)

## Chapter 7: Matrix Operations

Date
Entry Task
Activity
Assignments and Homework
1/5
For all students at your four tops, organize the following information into a matrix of data. Be sure to label all relevant details:
• # of writing utensils in your backpack
• # of notebooks in your backpack
• Your age to the nearest year
• Month in which you were born (Jan = 1, Feb = 2, Mar = 3, etc.)
Parts of a Matrix: Row, Column, Dimensions, elements/entries. Real world application of organizing data.

Student Organization Tool: Foldable

Read Matrix basics (pg. 428 - 432 up to "Addition and Subtraction of Matrices"). Add notes to Foldable.

JR: Explain how to organize data into a matrix. Provide a real world example.
Create a 3x3 matrix using data on a nutrition facts label from three packaged goods of your choosing.  The three rows represent calories, total fat, and protein, respectively.  The three columns will be the names of the packaged goods.  Provide the data for a single serving of each item.
1/6
Add the following matrix to the matrix you created for homework. What is the meaning of this addition?
Matrix addition, subtraction and scalar multiplication.

Pg. 432 - 433 (Matrix addition, subtraction and scalar multiplication). Add new information to Foldable.    Carry out each indicated operation, or explain why it cannot be performed.
• A + B
• C - D
• C + A
• 5A
JR: Explain the process for adding and subtracting matrices. Address the two requirements for adding or subtracting matrices. Provide an example.

Problem copied from Stewart, Redlin, Watson 3e Trigonometry and Algebra textbook, 2012.
1. Nutrition apps use matrices to store information about popular foods. Matrix A stores information for a pancake recipe. Mr. G. made an order of pancakes and Dr. Edge tripled his recipe. What is the combined nutrition for all pancakes made by Mr. G and Dr. Edge?
Note: Aunt Jemima pancake mix (1/3 cup), 1 large egg and 1 cup low fat milk. 2. Buckstars Coffee (BSC), an international coffee chain competes directly with Yllut's Coffee (YC). The following images are directly from the menu in the store.
• Organize two, 5 x 3 matrices for these menus (one matrix per coffee chain).
• Define each row and column.
• Calculate BSC - YC, explain the meaning of this difference.
1/7
(Block)
Yullut's coffee realized that want to increase prices by 2%. Use your matrix created from your homework to calculate their new coffee prices? POGIL to introduce matrix multiplication.

JR: Explain in simple language how to multiply the matrix and the vector. Provide the dimensions of the resulting matrix.
Pg. 436 #1, 4, 7
1/9
Recall the following properties from algebra, provide an algebraic example for each:
• Distributive Property
• Associative Property of Multiplication
• Commutative Property of Multiplication
More practice with matrix multiplication, addition and subtraction (Prove or disprove associative, distributive, and commutative property).

JR: Is the following equation true? Explain why or why not. Add titles for the last two "tabs" of your foldable. Add all relevant details within the first six "tabs".
• Matrix, Row, Column
• Dimension, Element
• Matrix Addition and Subtraction
• Scalar Multiplication
• Matrix Multiplication
• Matrix Properties
• Inverse Matrices
1/12
Recall the following properties from algebra, provide an algebraic example for each:
• Multiplicative Identity Property
• Multiplicative Inverse Property

Additionally, write the matrix equivalent of the properties above (or make a best guess if you are unsure).

Debrief Entry Task

The Multiplicative Inverse
; Activity 7.2 pg 441-442.

JR:Explain in simple language the purpose of a multiplicative inverse AND what it means to be an identity matrix.
Pg. 446 #1, 2, 3.  Set up the matrices to solve the problem posed at the beginning of Activity 7.2 (see page 441).

Consider studying for the semester final
1/13
Create the exact form of the inverse of the matrix. Inverse Matrices activity.

JR: Explain why this matrix does not have an inverse. Pg. 447-450 #7 and #11 (use inverse matrix to solve the systems).

Note: For part b, refer to Inverse Matrices activity from class.

Consider viewing the following website:
http://www.mathsisfun.com/algebra/matrix-inverse.html

Consider studying for the semester final
1/14
Another way to express a two dimensional vector is with a 2 X 1 matrix.
1. Draw the x-y plane and the following vector. 2. Now, perform the following matrix multiplication AND draw the result on the same x-y plane as part 1. 3. What happens to the vector after it is multiplied by the matrix?
Practice multiplying transformation matrices by vectors to "see" what happens to these.

Application of matrices with solving systems of equations.

Begin Final Review Exercises.

JR: Write about two uses for matrices or matrix operations. What are their real world applications?
Matrix Final Review Problems/Exercises
Pg. 436 # 10 (omit part e)
Pg. 447 #5 (calculator okay)
Pg. 461 #9 (omit b)
Pg. 463 #13b (use matrix operations, explain your process, calculator okay)
Pg. 464 #2, 5

Consider studying for the semester final
1/16
Write at least two questions you have about matrices, their uses or problems you need help solving.

Review Day: Reserved for reviewing any challenging concepts or misunderstandings.

JR: Which concepts about matrices do you need to continue reviewing for the unit exam next Friday? What steps will you take this weekend to study for the semester exam?
Develop a plan for study and review of precalculus for the semester 1 final exam.  Include:
• Selected passages to read.
• Recommended online lectures.
• Suggested problems.
• A method to share questions and solutions with ALL other class members.
Collaborate on THIS Google Doc. Do not delete others' work.

Consider studying for the semester final.

Recall the syllabus says "no late work will be accepted in the last five school days of a grading period."  That means NO LATE WORK from today 16 January) through the end of the semester!

Practice Matrix Exam (optional)
1/20
Write at least two explicit questions or concepts for which you are still uncertain or would like review.
Prepare for Semester 1 Final Exam

Review Student Questions

JR:
Prepare for the Final Exams.
1/21
Get ready for the exam!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.
Semester Final Exam 1.1: You may use YOUR calculator and a 3 x 5 note card* (writing on both sides is permitted).  Measurement devices (e.g. ruler and protractor) are also allowed.  Expect questions on all previous topics in the course (excluding matrix operations).  Specifically
• Data modeling.
• Trigonometry: right and non-right triangles; solving for unknown sides and angles.
• Vectors: flight plan; arithmetic of vectors; conversion between degrees and radians; and, modeling with parametric equations.
• Trigonometric functions: create a function that will trace a periodic graph.
*Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

Reminder: you will not be allowed to do "corrections" on the final exams!

JR: Google Reflection
Prepare for the remaining Final Exam.
1/23
Get ready for the exam!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.
Semester Final Exam 1.2: You may use a 3 x 5 note card* (writing on both sides is permitted).  Measurement devices (e.g. ruler and protractor) are also allowed.  Note: calculator NOT allowed!  Expect questions on matrices, specifically
• Organize and manipulate real world data.
• Interpret and perform addition, subtraction and multiplication.
• Create an inverse matrix.
*Note cards may not be mechanically reproduced (no photo copies, word processing, etc.).

Reminder: you will not be allowed to do "corrections" on the final exams!

JR: What are your goals (in general) between now and the end of the school year? What do you hope to learn in mathematics?