Unit 12 – Matrices Review Problems

Slides:



Advertisements
Similar presentations
Chapter 13 Eraser Game!.
Advertisements

Over Lesson 6–3. Splash Screen Solving Systems with Elimination Using Multiplication Lesson 6-4.
Word Problems.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Word Problems There were originally twice as many boys as girls in my Honors Geometry class. After three new girls join the class, the total number of.
EXAMPLE 1 Finding Perimeter and Area SOLUTION Find the perimeter. P = 2l + 2w Write formula. = 2 ( 8 ) + 2( 5 ) Substitute. = 26 Multiply, then add. Find.
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.
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.
EXAMPLE 4 Solve a multi-step problem CYCLING
Warm Up What is the LCM of 3x and –4x ? What is the LCM of 5y and 2y ?
Matrix Equations Step 1: Write the system as a matrix equation. A three-equation system is shown below.
Systems of Linear Equations in Two Variables
Copyright © Cengage Learning. All rights reserved. 6 Systems of Equations and Inequalities.
8.4 Word Problems Math 9.
Chapter 6 Systems of Linear Equations
1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Systems of Equations CHAPTER 1Solving Systems of Linear Equations Graphically.
Inverses and Systems Section Warm – up:
7.1 Systems of Linear Equations. Graphing Method Reminders 1. Write each equation in slope-intercept form 2.Graph each line on the coordinate plane 3.Label.
7.1 Systems of Linear Equations. Graphing Method Reminders 1. Write each equation in slope-intercept form 2.Graph each line on the coordinate plane 3.Label.
Copyright © 2011 Pearson Education, Inc. Systems of Linear Equations and Inequalities CHAPTER 9.1Solving Systems of Linear Equations Graphically 9.2Solving.
Can I use elimination to solve this system of equations? 2x + y = 23 3x + 2y = 37.
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,
Using Linear Systems to Solve Application Problems:  1. Define the variables. There will be two unknown values that you are trying to find. Give each.
Regents Review #2 Equations. What type of Equations do we need to solve? 1)Simple Equations 2)Equations with Fractions 3)Quadratic Equations 4)Literal.
CHAPTER 7 REVIEW SOLVING SYSTEMS OF EQUATIONS AND INEQUALITIES.
Preview Warm Up California Standards Lesson Presentation.
Unit 4 Rational functions
Solving Linear Systems Algebraically with Substitution Section 3-2 Pages
KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.
Warm Up Simplify each expression. 1. 3(10a + 4) – (20 – t) + 8t 3. (8m + 2n) – (5m + 3n) 30a t 3m – n 4. y – 2x = 4 x + y = 7 Solve by.
4.8 Using matrices to solve systems! 2 variable systems – by hand 3 or more variables – using calculator!
7.2 Two-Variable Linear Systems Elimination method.
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.
Lesson Menu Five-Minute Check (over Lesson 6-2) Then/Now New Vocabulary Key Concept:Invertible Square Linear Systems Example 1:Solve a 2 × 2 System Using.
Chapter Seven 7.2 – Systems of Linear Equations in Two Variables.
3.8B Solving Systems using Matrix Equations and Inverses.
Chapter 7 Trigonometry / Pre-Calculus
Ch. 7 – Matrices and Systems of Equations Elimination.
PreCalculus 7-R Unit 7 System of Equations and Matrices Review Problems.
Warm-up 1. Solve the following system of equations by graphing: 3x – y = -3 y – 3x = Determine the solution type from the following system of equations:
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 6: Systems of Equations and Matrices 6.1 Systems of Equations in Two Variables.
1) How many milliliters of a 40% silver nitrate solution must be mixed with 20.0 milliliters of a 25% silver nitrate solution to make a 34% solution? 2)
Systems of Linear Equations in Two Variables
Systems of Equations in Two Variables
Solving Equations & Inequalities
Solve the following word problem.
Finding Perimeter and Area
3.2 Applications of Systems of Equations
Review Problems Matrices
Solving Systems of Linear Equations
Section 8.1 Solving Systems of Linear Equations by Graphing.
Two-Variable Linear System
Applications of Linear Systems
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
3 Solving Application Problems.
Warm Up 3x + 5y = 25 4x + 7y = 34 Find the value of x and y so that both equations are true.
Use the substitution method to find all solutions of the system of equations {image} Choose the answer from the following: (10, 2) (2, 10) (5, - 2) ( -
Splash Screen.
Copyright © Cengage Learning. All rights reserved.
( 1, -2 ) ( -2, 1 ) ( -1, 1 ) ( 1, 1 ) ( t, 2t - 3 ) ( t, -1t - 2 )
Find the inverse of the matrix
Use Inverse Matrices to Solve 2 Variable Linear Systems
Chapter 1 – 3 Review!          .
Warm Up Solve for y y = 2x 2. 6x = 3y y = 2x – 3 y = 2x
Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz
Solving Linear Systems Using Inverses and Cramer’s Rule
Systems of Linear Equations in Two Variables (by Elimination)
College Algebra Chapter 5 Systems of Equations and Inequalities
one of the equations for one of its variables Example: -x + y = 1
Systems of Equations Solve by Graphing.
Presentation transcript:

Unit 12 – Matrices Review Problems PreCalculus 12-R

Solve the system of Equations (45, 9) Review Problems 1

Solve the system of Equations (–20, 5), (20, –5) Review Problems 2

Solve the system of Equations (3, 8) Review Problems 3

Solve the system of Equations (6, 3), (–6, 3), (6, –3), (–6, –3) Review Problems 4

Two equations and their graphs are given Two equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system. (8, 3), (0, –1) Review Problems 5

Solve the system of Equations (1, 0), (–1, 0) Review Problems 6

Solve the system of Equations Review Problems 7

Solve the system of Equations (6, 3) Review Problems 8

Solve the system of Equations Review Problems 9

Solve the system of Equations Review Problems 10

x = –3, y = 4, z = –1 Review Problems 11 Use back-substitution to solve the triangular system. x = –3, y = 4, z = –1 Review Problems 11

Write the system of equations that corresponds to the matrix. Review Problems 12

No Determine whether the matrices A and B are equal. Review Problems 13

Perform the matrix operation. The matrix operation is impossible Review Problems 14

Solve the matrix equation 2X – A = B for the unknown matrix X, if Review Problems 15

Find A + B if Review Problems 16

Find C(AB) if Review Problems 17

Find AB+AC, if Review Problems 18

Solve the system. (42, 6) Review Problems 19

Solve the system. (10, 8) Review Problems 20

Review Problems 21

Review Problems 22

Review Problems 23

Review Problems 24

Review Problems 25

Review Problems 26

Review Problems 27

Review Problems 28

Review Problems 29

length is 40 cm, width is 21 cm Review Problems 30 A rectangle has an area of 840 cm2 and a perimeter of 122 cm. What are its dimensions? length is 40 cm, width is 21 cm Review Problems 30

2 dimes, 10 quarters Review Problems 31 A man has 12 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.70, how many dimes and how many quarters does he have? 2 dimes, 10 quarters Review Problems 31

A man flies a small airplane from Fargo to Bismarck, North Dakota, a distance of 180 miles. Because he is flying into a headwind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 15 minutes. What is his speed in still air, and how fast is the wind blowing? speed in still air is 117 mi/h, the wind is blowing 27 mi/h Review Problems 32

A biologist has two brine solutions, one containing 10% salt and another containing 25% salt. How many milliliters of each solution should she mix to obtain 1 L of a solution that contains 23.5% salt? 100 milliliters of the first brine solution, 900 milliliters of the second brine solution Review Problems 33

Find the complete solution of the linear system, if possible. The system is inconsistent. Review Problems 34

Find the complete solution of the linear system, if possible. x = 5t + 2, y = 2t +2, z = t Review Problems 35

Find the inverse of the matrix. Review Problems 36

Find the inverse of the matrix. Review Problems 37

Find the inverse of the matrix. Review Problems 38

Find the inverse of the matrix. Review Problems 39

Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix x = 10, y = -13 Review Problems 40

Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix x = –3, y = 1 Review Problems 41

x = 1, y = -2, z = -1 Review Problems 42 Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix x = 1, y = -2, z = -1 Review Problems 42

Use a calculator that can perform matrix operations to solve the system x = 4, y = 24, z = 8 Review Problems 43

Solve the matrix equation by multiplying each side by the appropriate inverse matrix. Review Problems 44

Find the inverse of the matrix. Review Problems 45

Find the inverse of the matrix. Review Problems 46

Find the inverse of the matrix. Review Problems 47

Identify the matrix which does not have an inverse. Review Problems 48

Solve the system. x = 9, y = 1, z = –21 Review Problems 49

Solve the system. x = 2, y = 7, z = 7, w –6 Review Problems 50

Answers x = –3, y = 4, z = –1 No (6, 3) (45, 9) (–20, 5), (20, –5) (3, 8) No (6, 3), (–6, 3), (6, –3), (–6, –3) The matrix operation is impossible (8, 3), (0, –1) (1, 0), (–1, 0) (6, 3) Answers

Answers (42, 6) (10, 8) 2 dimes, 10 quarters length is 40 cm, width is 21 cm 2 dimes, 10 quarters speed in still air is 117 mi/h, the wind is blowing 27 mi/h 100 milliliters of the first brine solution, 900 milliliters of the second brine solution The system is inconsistent. Answers

Answers x = –3, y = 1 x = 1, y = -2, z = -1 A x = 5t + 2, y = 2t +2, z = t A x = 4, y = 24, z = 8 x = 10, y = -13 x = –3, y = 1 x = 9, y = 1, z = –21 x = 1, y = -2, z = -1 x = 2, y = 7, z = 7, w –6 Answers