Advanced Algebra II Notes 6.4 Solving Systems with Inverse Matrices Solve the system of equations using elimination: 2x + y = 5 5x + 3y = 13 Write the.

Slides:

Advertisements

Similar presentations

4.5 Inverses of Matrices.

Advertisements

MATRICES Using matrices to solve Systems of Equations.

Using Matrices to Solve a 3-Variable System

Use an inverse matrix to solve the linear system.

Using Inverse Matrices Solving Systems. You can use the inverse of the coefficient matrix to find the solution. 3x + 2y = 7 4x - 5y = 11 Solve the system.

Using Matrices to Solve a System of Equations. Multiplicative Identity Matrix The product of a square matrix A and its identity matrix I, on the left.

Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.

Algebra 2: Lesson 5 Using Matrices to Organize Data and Solve Problems.

4-6 Row Operations and Augmented Matrices Warm Up Lesson Presentation

THU, JAN 8, 2015 Create a “Big Book of Matrices” flip book using 4 pages. Do not make your tabs big! BIG BOOK OF MATRICES What is a Matrix? Adding & Subtracting.

4.5 Solving Systems using Matrix Equations and Inverses.

4.4 & 4.5 Notes Remember: Identity Matrices: If the product of two matrices equal the identity matrix then they are inverses.

Inverses and Systems Section Warm – up:

4.5 Solving Systems using Matrix Equations and Inverses OBJ: To solve systems of linear equations using inverse matrices & use systems of linear equations.

Inverse Matrices and Systems

HW: Pg. 219 #16-26e, 31, 33. HW: Pg #37, 41, 45, 49, 59.

4-7 Inverse Matrices & Systems

Holt Algebra Matrix Inverses and Solving Systems A matrix can have an inverse only if it is a square matrix. But not all square matrices have inverses.

4-5 Matrix Inverses and Solving Systems Warm Up Lesson Presentation

Objectives Determine whether a matrix has an inverse.

Lesson 6.3.  Three friends, Duane, Marsha, and Parker, decide to take their younger siblings to the movies. Before the movie, they buy some snacks at.

Do Now: Evaluate: 3AB. Algebra II 3.7: Evaluate Determinants HW: p.207 (4-14 even) Test : Friday, 12/6.

Lesson 7.6 & 7.7 Inverses of a Square Matrix & Determinant.

Find the determinant of this matrix Jeff buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buy 5 apples and 9 pears for $10.40.

1.10 and 1.11 Quiz : Friday Matrices Test: Oct. 20.

1. Inverse of A 2. Inverse of a 2x2 Matrix 3. Matrix With No Inverse 4. Solving a Matrix Equation 1.

4.7 Identity and Inverse Matrices and Solving Systems of Equations Objectives: 1.Determine whether two matrices are inverses. 2.Find the inverse of a 2x2.

Advanced Trig Exam Review Day Three: Matrices. Solving Systems of Equations.

Inverse and Identity Matrices Can only be used for square matrices. (2x2, 3x3, etc.)

Have we ever seen this phenomenon before? Let’s do some quick multiplication…

Transparency 5 Click the mouse button or press the Space Bar to display the answers.

Dr. Shildneck Fall, 2015 SOLVING SYSTEMS OF EQUATIONS USING MATRICES.

Ch 8 Equations and Inequalities

4.7 Solving Systems using Matrix Equations and Inverses

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.

Warm up. Solving Systems Using Inverse Matrices Systems to Matrices A system of equations in standard form (Ax+By=C) can be written in matrix form [A][X]=[B]

Chapter 4 Section 5 and 6 Finding and Using Inverses Algebra 2 Notes February 26, 2009.

3.8B Solving Systems using Matrix Equations and Inverses.

Warm Up Multiply the matrices. 1. Find the determinant. 2. –1 Welcome! I’m so glad you’re here! Please get your Calculator. Please get started on this.

(4-2) Adding and Subtracting Matrices Objectives: To Add and subtract Matrices To solve certain Matrix equations.

Algebra 1 Section 3.4 Solve equations with variables on both sides of the equation. Solve: 17 – 2x = x Solve 80 – 9y = 6y.

Equations with Variables on Both Sides Chapter 3 Section 3.

Using Matrices to Solve a 3-Variable System

16 Matrix Inverses and Solving Systems Lesson Presentation Lesson Quiz.

College Algebra Chapter 6 Matrices and Determinants and Applications

Use Inverse Matrices to Solve Linear Systems

PreCalculus Section 14.3 Solve linear equations using matrices

12-4: Matrix Methods for Square Systems

Review Problems Matrices

Solving Equations: The Multiplication Principle

Section 6.4 Multiplicative Inverses of Matices and Matrix Equations

Use Inverse Matrices to Solve Linear Systems

Solving Linear Systems Using Inverse Matrices

Chapter 7: Matrices and Systems of Equations and Inequalities

Multiplicative Inverses of Matrices and Matrix Equations

Use Inverse Matrices to Solve 2 Variable Linear Systems

Find the area of the Triangle

ALGEBRA I - SECTION 2-3 (Solving Multi-Step Equations)

Inverse Matrices and Systems

Section 9.4 Multiplicative Inverses of Matices and Matrix Equations

3.6 Solving Systems with Three Variables

Bellwork 1) Multiply. 3) Find the determinant. 2) Multiply.

Solving Systems of Equations Using Matrices

1.11 Use Inverse Matrices to Solve Linear Systems

Matrix Multiplication

Using matrices to solve Systems of Equations

Day 83 – Business Project.

Solving Linear Systems of Equations - Inverse Matrix

Presentation transcript:

Advanced Algebra II Notes 6.4 Solving Systems with Inverse Matrices Solve the system of equations using elimination: 2x + y = 5 5x + 3y = 13 Write the system as the product of a coefficient matrix and a variable matrix equal to a constant matrix.

This equation is a matrix form of ax = b What is the multiplicative identity? What is the identity matrix for State the identity matrices for each dimension: 1x12x23x34x4

Find the inverse matrix for

Solve the given system using an inverse matrix: 2x + 3y = 7 x + 4y = 6

On a recent trip to the movies, Duane, Marsha, and Parker each purchased snacks. Duane bought two candy bars, a small drink, and two bags of popcorn for a total of $ Marsha spent $9.00 on a candy bar, two small drinks, and a bag of popcorn. Parker spent $12.35 on two small drinks and three bags of popcorn, but no candy. (poor Parker, no candy). If all the prices included tax, what was the price of each item?

Assignment: page 331: