Alg 2 - Chapter 4 Jeopardy Matrix Operations

Slides:



Advertisements
Similar presentations
Multiplication and Division
Advertisements

8 2.
Warm-Up (Over 4.5) [1]Evaluate Calculator Free: [2]Find the area of a triangle whose vertices are at (9, 0) (-3, 10) and (5, -6).
Jeopardy Start Final Jeopardy Question Category 1Category 2Category 3Category 4Category
Back to menu category 1 type you categories here– delete these instructions. Final jeopardy question.
Powerpoint Jeopardy Category 1Category 2Category 3Category 4Category
Chapter 4 Systems of Linear Equations; Matrices
Chapter 5 The Mathematics of Diversification
EXAMPLE 3 Use Cramer’s rule for a 2 X 2 system
4.5 Determinants and Cramer’s Rule. Objectives Evaluate a determinant of a 2 x 2 matrix. Use Cramer’s rule for linear equations.
Using Matrices to Solve a 3-Variable System
EXAMPLE 2 Solve a matrix equation SOLUTION Begin by finding the inverse of A = Solve the matrix equation AX = B for the 2 × 2 matrix X. 2 –7 –1.
Section 8.3 – Systems of Linear Equations - Determinants Using Determinants to Solve Systems of Equations A determinant is a value that is obtained from.
4-6 3x3 Matrices, Determinants, & Inverses
4.5, x 2 and 3 x 3 Matrices, Determinants, and Inverses Date: _____________.
Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.
3.5 Solution by Determinants. The Determinant of a Matrix The determinant of a matrix A is denoted by |A|. Determinants exist only for square matrices.
Academy Algebra II/Trig
Objective: Students will solve systems of equations using inverse matrices.
EXAMPLE 1 Evaluate determinants Evaluate the determinant of the matrix. a SOLUTION b – – – –
MAC 1140 Unit 4 Test Review. 1. Give the order of the following matrix:.
Chapter 8 By Briana, Brandon, Kyle, and Michaela.
Determinants, Inverse Matrices & Solving. Notice the different symbol: the straight lines tell you to find the determinant!! (3 * 4) - (-5 * 2) 12 - (-10)
Solving Using Matrices By Helen Chin Kitty Luo Anita La.
4-8 Augmented Matrices and Systems
Copyright © 2007 Pearson Education, Inc. Slide 7-1.
HW: Pg. 219 #16-26e, 31, 33. HW: Pg #37, 41, 45, 49, 59.
Identity and Inverse Matrices Solving Systems Using Inverse Matrices
Copyright © 2009 Pearson Education, Inc. CHAPTER 9: Systems of Equations and Matrices 9.1 Systems of Equations in Two Variables 9.2 Systems of Equations.
Do Now: Evaluate: 3AB. Algebra II 3.7: Evaluate Determinants HW: p.207 (4-14 even) Test : Friday, 12/6.
2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4pt 5 pt 1pt Row Operations Matrix Operations.
Identity What number is the multiplication identity for real numbers? For matrices, n x n--square matrices, has 1’s on main diagonal and zeros elsewhere.
13.6 MATRIX SOLUTION OF A LINEAR SYSTEM.  Examine the matrix equation below.  How would you solve for X?  In order to solve this type of equation,
Inverse and Identity Matrices Can only be used for square matrices. (2x2, 3x3, etc.)
Chapter 9 Matrices and Determinants Copyright © 2014, 2010, 2007 Pearson Education, Inc Determinants and Cramer’s Rule.
4.3 Determinants and Cramer’s rule How do you find the determinant of a matrix? How do you find the area of a triangle given 3 sets of coordinates? How.
Section 10.3 and Section 9.3 Systems of Equations and Inverses of Matrices.
4-8 Augmented Matrices & Systems. Objectives Solving Systems Using Cramer’s Rule Solving Systems Using Augmented Matrices.
4.1: Matrix Operations Objectives: Students will be able to:
GUIDED PRACTICE for Example – – 2 12 – 4 – 6 A = Use a graphing calculator to find the inverse of the matrix A. Check the result by showing.
Chapter 7 Solving systems of equations substitution (7-1) elimination (7-1) graphically (7-1) augmented matrix (7-3) inverse matrix (7-3) Cramer’s Rule.
Notes Over 10.5 Using Cramer’s Rule for a 2 x 2 System
Copyright © 1999 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen College Algebra, 6 th Edition Chapter Seven Matrices & Determinants.
3.8B Solving Systems using Matrix Equations and Inverses.
Notes Over 4.3 Evaluate Determinants of 2 x 2 Matrices
Do Now: Perform the indicated operation. 1.). Algebra II Elements 11.1: Matrix Operations HW: HW: p.590 (16-36 even, 37, 44, 46)
Copyright © 2001 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen Precalculus: Functions & Graphs, 5 th Edition Chapter Nine Matrices & Determinants.
Using Matrices to Solve a 3-Variable System
Use Inverse Matrices to Solve Linear Systems
Determinants.
Answer the FRONT of the worksheet that was passed out yesterday!
Review Problems Matrices
Barnett/Ziegler/Byleen College Algebra, 7th Edition
Warmup: Find the product, if possible. −6 4 − 
الوحدة السابعة : المصفوفات . تنظيم البيانات فى مصفوفات . الوحدة السابعة : المصفوفات . تنظيم البيانات فى مصفوفات . 1 جمع المصفوفات وطرحها.
Solve System by Linear Combination / Addition Method
Solving Linear Systems Using Inverse Matrices
Evaluate Determinants & Apply Cramer’s Rule
Chapter 7: Matrices and Systems of Equations and Inequalities
Using matrices to solve Systems of Equations
Use Inverse Matrices to Solve 2 Variable Linear Systems
Inverse & Identity MATRICES Last Updated: October 12, 2005.
Find the area of the Triangle
3.8 Use Inverse Matrices to Solve Linear Systems
Chapter 7: Matrices and Systems of Equations and Inequalities
4.4 Objectives Day 1: Find the determinants of 2  2 and 3  3 matrices. Day 2: Use Cramer’s rule to solve systems of linear equations. Vocabulary Determinant:
4.3 Determinants and Cramer’s Rule
Solving Systems of Equations Using Matrices
Chapter 7 Review! Systems of Equations.
Solving a System of Linear Equations
Presentation transcript:

Alg 2 - Chapter 4 Jeopardy 10 20 30 40 50 Matrix Operations Multiplying Matrices Determinants, Area of Triangle & Cramer's Rule Identity and Inverse Matrices Solving Systems Using Inverse Matrices 10 20 30 40 50

10 points Category 1 - 10

10 points - Answer Category 1 - 10

Perform the indicated operation. 20 points Perform the indicated operation. Category 1 - 20

Perform the indicated operation. 20 points - Answer Perform the indicated operation. Category 1 - 20

Perform the indicated operation. 30 points Perform the indicated operation.

Perform the indicated operation. 30 points - Answer Perform the indicated operation.

40 points Solve the matrix equation for x and y.

40 points - Answer Solve the matrix equation for x and y.

50 points Solve the matrix equation for x and y.

50 points - Answer Solve the matrix equation for x and y.

10 points

10 points - Answer

Perform the indicated operation. 20 points Perform the indicated operation.

Perform the indicated operation. 20 points - Answer Perform the indicated operation.

Perform the indicated operation. 30 points Perform the indicated operation.

Perform the indicated operation. 30 points - Answer Perform the indicated operation.

Perform the indicated operation. 40 points Perform the indicated operation.

Perform the indicated operation. 40 points - Answer Perform the indicated operation.

Perform the indicated operation. 50 points Perform the indicated operation.

Perform the indicated operation. 50 points - Answer Perform the indicated operation.

10 points NO CALCULATOR!

10 points - Answer NO CALCULATOR!

Evaluate the determinant of the matrix. 20 points NO CALCULATOR! Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix. 20 points - Answer NO CALCULATOR! Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix. 30 points NO CALCULATOR! Evaluate the determinant of the matrix.

Evaluate the determinant of the matrix. 30 points - Answer NO CALCULATOR! Evaluate the determinant of the matrix.

Find the area of the triangle with the given vertices. 40 points NO CALCULATOR! Find the area of the triangle with the given vertices.

Find the area of the triangle with the given vertices. 40 points - Answer NO CALCULATOR! Find the area of the triangle with the given vertices.

You MAY use a CALCULATOR! 50 points You MAY use a CALCULATOR! Use Cramer's rule to solve the linear system. Show what you are entering in your calculator.

50 points - Answer You MAY use a CALCULATOR! Use Cramer's rule to solve the linear system. Show what you are entering in your calculator.

Write the identity 3x3 matrix 10 points Write the identity 3x3 matrix

Write the identity 3x3 matrix 10 points - Answer Write the identity 3x3 matrix

20 points NO CALCULATOR!

20 points - Answer

Find the inverse of the matrix. SHOW WORK! 30 points NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

Find the inverse of the matrix. SHOW WORK! 30 points - Answer NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

Find the inverse of the matrix. SHOW WORK! 40 points NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

Find the inverse of the matrix. SHOW WORK! 40 points - Answer NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

Find the inverse of the matrix. SHOW WORK! 50 points NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

Find the inverse of the matrix. SHOW WORK! 50 points - Answer NO CALCULATOR! Find the inverse of the matrix. SHOW WORK!

You MAY use a CALCULATOR! 10 points You MAY use a CALCULATOR! Solve the matrix equation. Show what you are entering in your calculator.

You MAY use a CALCULATOR! 10 points - Answer You MAY use a CALCULATOR! Solve the matrix equation.Show what you are entering in your calculator.

3x – 7y = -16 -2x + 4y = 8 20 points You MAY use a CALCULATOR! Use an inverse matrix to solve the linear system. 3x – 7y = -16 -2x + 4y = 8

You MAY use a CALCULATOR! 20 points - Answer You MAY use a CALCULATOR! Use an inverse matrix to solve the linear system 3x – 7y = -16 -2x + 4y = 8

2x + 3y = -8 x + 2y = -3 30 points You MAY use a CALCULATOR! Use an inverse matrix to solve the linear system. 2x + 3y = -8 x + 2y = -3

You MAY use a CALCULATOR! 30 points - Answer You MAY use a CALCULATOR! Use an inverse matrix to solve the linear system. 2x + 3y = -8 x + 2y = -3

40 points Skating Party - Your planning a birthday party for your younger brother at a skating rink. The cost of admission is $3.50 per adult and $2.25 per child, and there is a limit of 20 people. You have $50 to spend. Use an inverse matrix to determine how many adults and how many children you can invite.

40 points - Answer Skating Party - Your planning a birthday party for your younger brother at a skating rink. The cost of admission is $3.50 per adult and $2.25 per child, and there is a limit of 20 people. You have $50 to spend. Use an inverse matrix to determine how many adults and how many children you can invite.

50 points Stock Investment – You have $9000 to invest in three Internet companies listed on the stock market. You expect the annual returns for companies A, B, and C to be 10%, 9%, and 6%, respectively. You want the combined investment in companies B and C to be twice that of company A. How much should you invest in each company to obtain an average return of 8%?

50 points - Answer Stock Investment – You have $9000 to invest in three Internet companies listed on the stock market. You expect the annual returns for companies A, B, and C to be 10%, 9%, and 6%, respectively. You want the combined investment in companies B and C to be twice that of company A. How much should you invest in each company to obtain an average return of 8%?