WUPS: Find the determinates by hand

Slides:

Advertisements

Similar presentations

4.5 Inverses of Matrices.

Advertisements

Matrix Revolutions: Solving Matrix Equations Matrix 3 MathScience Innovation Center Betsey Davis

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

Using Matrices to Solve a 3-Variable System

A Fast Introduction inverse matrix1 What is a matrix (One Matrix many matrices) Why do they exist Matrix Terminology Elements Rows Columns Square.

12.4 Inverses of Matrices. Remember if A and B are inverses, AB = I and BA = I *only square matrices can have multiplicative inverses* Ex 1) Show that.

Use an inverse matrix to solve the linear system.

3.8 – Use Inverse Matrices to Solve Linear Systems The n x n identity matrix is a matrix with 1’s on the main diagonal and 0’s elsewhere. If A is any n.

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.

Name: _________________________ Wups 3. Corrected By: _________________________.

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.

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

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

Objectives Determine whether a matrix has an inverse.

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

8.3 Another Way of Solving a System of Equations Objectives: 1.) Learn to find the inverse matrix 2.) Use the inverse matrix to a system of equations.

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.

Inverse Matrices and Matrix Equations Dr. Shildneck Fall, 2015.

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.

Warm Up. Inverse Matrices Three main topics today Identity Matrix Determinant Inverse Matrix.

Chapter 4 Section 4: Inverse and Identity Matrices 1.

Objectives  Find the inverse of a matrix  Find matrix inverses with technology  Solve matrix equations  Solve matrix equations with technology Inverse.

Warm-Up 3) Find the determinant by hand. 4) Find the determinant using your calculator. 1) Multiply. Show work. 2) Multiply. Show work.

Identity & Inverse Matrices

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

Warm- Up Solve the following systems using elimination or substitution : 1. x + y = 6 -3x + y = x + 4y = 7 x + 2y = 7.

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.

More on Matrices Quiz : Friday, Oct. 16 Unit 1 Test: Oct. 23 ( tentative ) WOTD: affable: adj: courteous and pleasant, sociable, easy to speak.

2.5 – Determinants and Multiplicative Inverses of Matrices.

Use Inverse Matrices to Solve Linear Systems Objectives 1.To find the inverse of a square matrix 2.To solve a matrix equation using inverses 3.To solve.

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.

Warm Up Multiple the matrices. 1. Find the determinant –1 0.

If A and B are both m × n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding elements of A and B. add these.

Chapter Seven Linear Systems and Matrices. Warm-up #1 The University of Georgia and Florida State University scored a total of 39 points during the 2003.

Using Matrices to Solve a 3-Variable System

College Algebra Chapter 6 Matrices and Determinants and Applications

Use Inverse Matrices to Solve Linear Systems

12-4: Matrix Methods for Square Systems

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

Chapter 4 Systems of Linear Equations; Matrices

Ch. 7 – Matrices and Systems of Equations

The Inverse of a Square Matrix

Inverse of a Square Matrix

Multiplication of Matrices

Solving Systems in 3 Variables using Matrices

Warm-Up BC 3. |A|.

Matrix Algebra.

Matrix Algebra.

Name: _________________________

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

Use Inverse Matrices to Solve Linear Systems

More about Matrices Chapter 4, Sections 5, 7.

WUPS: Find the determinates by hand

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

Unit 3: Matrices

Find the area of the Triangle

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

Inverse of a Matrix Solving simultaneous equations.

1.11 Use Inverse Matrices to Solve Linear Systems

Solving Linear Systems of Equations - Inverse Matrix

Presentation transcript:

WUPS: Find the determinates by hand Name: _____________ WUPS: Find the determinates by hand 1. 3.8 Warm-ups 2. Corrected By: ______________________________

4.5 Use Inverse Matrices to Solve Matrix Equations By the end you should: 1. find the inverse of a 2 x 2 and 3 x 3 matrix 2. solve a matrix equation Identity Matrix: a square matrix (n x n) with 1's as its main diagonal and zeros everywhere else. 2 x 2 IM If a matrix is multiplied by an identity matrix, then you will get the matrix. Similar to multiplying a number by one. 3 x 3 IM

Inverse Matrices 1) 2 matrices are inverses of each other if their product (in both orders) equals the identity matrix. ex. AB = I and BA = I a matrix can only have an inverse if it is square its determinant does not equal zero (Remember: you may NEVER divide by 0)

Inverse of a 2x2 Matrix The Inverse of matrix is

….to find the inverse of a matrix (2 x 2) Let’s try some:

….to find the inverse of a 3 x 3 matrix using your calculator On your calculator….. Enter the 3 x 3 matrix Select matrix from the home screen Press ENTER What do you get?

Solve a Matrix Equation How would you normally solve for x? AX = B When you have a matrix you cannot “divide” by a matrix, so you take the ________________.

Your turn: solve the matrix equation

Solve a Linear System Solve the following linear system: 2x – 3y = 19 Step 1: write as a matrix equation AX = B coefficient · matrix of = matrix of matrix (A) variables (X) constants (B) Step 2: find the inverse of A Step 3: solve for X

Your turn: 1. -2x + 3y = -11 5x + y = 19 2. 4x + y = 10 3x + 5y = -1 Calculator: Enter A and B Your turn: 1. -2x + 3y = -11 5x + y = 19 2. 4x + y = 10 3x + 5y = -1 3. –x – 2y + 4z = -28 x + y + 2z = -11 2x + y – 3z = 30

Yeah….more word problems! At a video store, the cost of 3 DVDs, 2 video games, and 4 VHS movies is $130. The cost of 2 DVDs, 1 video game, and 5 VHS movies is $105. The cost of 3 DVDs, 3 video games, and 3 VHS movies is $135. Find the cost of each item.

…you must be able to solve by hand!!! Homework: 3.8 pg. 214 (3-29 odd, 35-37, 44) **** Do #3-11 SOLVE BY HAND Show ALL your work Beware... …you must be able to solve by hand!!!

Find the inverse BY HAND Exit Card 3.8 Name: ________________________ Find the inverse BY HAND Solve the system of linear equations using matrices 3x – 2y = 5 6x – 5y = 14