Use Inverse Matrices to Solve 2 Variable Linear Systems

Slides:

Advertisements

Similar presentations

Solving Linear Equations Rule 7 ‑ 1: We can perform any mathematical operation on one side of an equation, provided we perform the same operation on the.

Advertisements

MATRICES Using matrices to solve Systems of Equations.

Solving Multiplication and Division Equations Lesson 2-7.

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.

4.7 Inverse Matrices and Systems. 1) Inverse Matrices and Systems of Equations You have solved systems of equations using graphing, substitution, elimination…oh.

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.

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

Gabriel Cramer was a Swiss mathematician ( )

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.

1.3 “Solving Linear Equations” Steps: 1.Isolate the variable. 2.To solve when there is a fraction next to a variable, multiply both sides by the reciprocal.

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

4-8 Augmented Matrices and Systems

4.6 Cramer’s Rule Using Determinants to solve systems of equations.

4-7 Inverse Matrices & Systems

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.

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,

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

Use the Distributive Property to: 1) simplify expressions 2) Solve equations.

Using Equations to Solve Percent Problems

Math – The Multiplication/Division Principle of Equality 1.

4.7 Solving Systems using Matrix Equations and Inverses

4.8 Using matrices to solve systems! 2 variable systems – by hand 3 or more variables – using calculator!

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.

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]

4-8 Cramer’s Rule We can solve a system of linear equations that has a unique solution by using determinants and a pattern called Cramer’s Rule (named.

Notes Over 10.5 Using Cramer’s Rule for a 2 x 2 System

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

3.8B Solving Systems using Matrix Equations and Inverses.

Notes Over 4.3 Evaluate Determinants of 2 x 2 Matrices

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.

Using Matrices to Solve a 3-Variable System

Use Inverse Matrices to Solve Linear Systems

Daily Vocabulary Coefficient matrix Matrix of constants.

TYPES OF SOLUTIONS SOLVING EQUATIONS

Cramer’s Rule (because Cramer RULES!)

Answer the FRONT of the worksheet that was passed out yesterday!

6) x + 2y = 2 x – 4y = 14.

TYPES OF SOLUTIONS SOLVING EQUATIONS

Solve Systems of Equations by Elimination

Solve for variable 3x = 6 7x = -21

Using Determinants to solve systems of equations

Lesson 13-3: Determinants & Cramer’s Rule

Use Inverse Matrices to Solve Linear Systems

Solving Linear Systems Using Inverse Matrices

Evaluate Determinants & Apply Cramer’s Rule

Write your agenda message No warm-up today Turn in:

Chapter 7: Matrices and Systems of Equations and Inequalities

Using matrices to solve Systems of Equations

Find the inverse of the matrix

Multiplicative Inverses of Matrices and Matrix Equations

Students will write a summary explaining how to use Cramer’s rule.

Find the area of the Triangle

Inverse Matrices and Systems

3.8 Use Inverse Matrices to Solve Linear Systems

Solving Multiplication Equations

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:

Solving Division Equations

Solving Systems of Equations Using Matrices

Inverse Matrices and Systems

1.11 Use Inverse Matrices to Solve Linear Systems

Using matrices to solve Systems of Equations

Algebraic Expressions & Solving Equations

Matrices and Linear Equations

Solving Linear Systems of Equations - Inverse Matrix

Presentation transcript:

Use Inverse Matrices to Solve 2 Variable Linear Systems Notes 3.8 (Day 2) Use Inverse Matrices to Solve 2 Variable Linear Systems

Using an inverse matrix to solve a linear system of equations: Step 1: Make a 2 x 2 coefficient matrix (just like in Cramer’s Rule) Step 2: Multiply the coefficient matrix by a 2 x 1 matrix, Step 3: Set this expression equal to the 2 x 1 matrix of constants Step 4: Find the inverse of the coefficient matrix and multiply both sides of the equation by the inverse Step 5: The result should give you = Step 6: Label the answer (x, y)

Use an inverse matrix to solve the linear system.

Use an inverse matrix to solve the linear system.

Use an inverse matrix to solve the linear system.

Homework: P 215 25-33