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Math Algebra Elementary Linear Algebra - Text Only (Looseleaf)

Gasoline Sales Matrix A shows the numbers of gallons of 87 − octane, 89 − octane, and 93 − octane gasoline sold at a convenience store over a weekend. 87 89 93 ︷ Octane A = [ 580 840 320 560 420 160 860 1020 540 ] Friday Saturday Sunday Matrix B gives the selling prices (in dollars per gallon) and the profits (in dollars per gallon) for the three grades of gasoline. Selling price Profit B = [ b 11 0.05 b 21 0.08 b 31 0.10 ] 87 89 93 } Octane (a) Find A B and interpret the result. (b) Find the convenience store’s profit from gasoline sales for the weekend.

Gasoline Sales Matrix A shows the numbers of gallons of 87 − octane, 89 − octane, and 93 − octane gasoline sold at a convenience store over a weekend. 87 89 93 ︷ Octane A = [ 580 840 320 560 420 160 860 1020 540 ] Friday Saturday Sunday Matrix B gives the selling prices (in dollars per gallon) and the profits (in dollars per gallon) for the three grades of gasoline. Selling price Profit B = [ b 11 0.05 b 21 0.08 b 31 0.10 ] 87 89 93 } Octane (a) Find A B and interpret the result. (b) Find the convenience store’s profit from gasoline sales for the weekend.

Solution Summary: The author explains that matrix A shows the numbers of gallons of 87- octane gasoline sold over a weekend.

Elementary Linear Algebra - Text Only (Looseleaf)

Elementary Linear Algebra - Text Only (Looseleaf)

8th Edition

ISBN: 9781305953208

Author: Larson

Publisher: Cengage Learning

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Textbook Question

Chapter 2.CR, Problem 51CR

Gasoline Sales Matrix A shows the numbers of gallons of 87 − octane, 89 − octane, and 93 − octane gasoline sold at a convenience store over a weekend.

87 89 93 ︷ Octane A = [ 580 840 320 560 420 160 860 1020 540 ] Friday Saturday Sunday

Matrix B gives the selling prices (in dollars per gallon) and the profits (in dollars per gallon) for the three grades of gasoline.

Selling price Profit B = [ b 11 0.05 b 21 0.08 b 31 0.10 ] 87 89 93 } Octane

(a) Find A B and interpret the result.

(b) Find the convenience store’s profit from gasoline sales for the weekend.

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Chapter 2.CR, Problem 50CR

Chapter 2.CR, Problem 52CR

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Chapter 2 Solutions

Elementary Linear Algebra - Text Only (Looseleaf)

Ch. 2.1 - Equality of Matrices In Exercises 1-4, find x and...Ch. 2.1 - Equality of Matrices In Exercises 1-4, find x and...Ch. 2.1 - Equality of Matrices In Exercises 1-4, find x and...Ch. 2.1 - Equality of Matrices In Exercises 1-4, find x and...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...Ch. 2.1 - Operations with Matrices In Exercises 5-10, find,...

Ch. 2.1 - Find a c21 and b c13, where C=2A-3B, A=544-312,...Ch. 2.1 - Find a c23 and b c32, where C=5A+2B,...Ch. 2.1 - Solve for x,y and z in the matrix equation...Ch. 2.1 - Solve for x,y,z and w in the matrix equation...Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Finding Products of Two Matrices In Exercises...Ch. 2.1 - Finding Products of Two Matrices In Exercises...Ch. 2.1 - Finding Products of Two Matrices In Exercises...Ch. 2.1 - Finding Products of Two Matrices In Exercises...Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Matrix Size In Exercises 29-36, let A,B,C,D,andE...Ch. 2.1 - Solving a Matrix Equation In Exercises 37 and 38,...Ch. 2.1 - Solving a Matrix Equation In Exercises 37 and 38,...Ch. 2.1 - Prob. 39E Ch. 2.1 - Solving a System of Linear Equations In Exercises...Ch. 2.1 - Solving a System of Linear Equations In Exercises...Ch. 2.1 - Prob. 42E Ch. 2.1 - Solving a System of Linear Equations In Exercises...Ch. 2.1 - Solving a System of Linear Equations In Exercises...Ch. 2.1 - Prob. 45E Ch. 2.1 - Solving a System of Linear Equations In Exercises...Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Writing a Linear Combination In Exercises 49-52,...Ch. 2.1 - Writing a Linear Combination In Exercises 49-52,...Ch. 2.1 - Writing a Linear Combination In Exercises 49-52,...Ch. 2.1 - Prob. 52E Ch. 2.1 - Solving a Matrix Equation In Exercises 53 and 54,...Ch. 2.1 - Solving a Matrix Equation In Exercises 53 and 54,...Ch. 2.1 - Solving a Matrix Equation In Exercises 55 and 56,...Ch. 2.1 - Solving a Matrix Equation In Exercises 55 and 56,...Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Finding Product of Diagonal Matrices In Exercises...Ch. 2.1 - Finding Product of Diagonal Matrices In Exercises...Ch. 2.1 - Guide Proof Prove that if A and B are diagonal...Ch. 2.1 - Prob. 62E Ch. 2.1 - Trace of a matrix In Exercises 63-66, find the...Ch. 2.1 - Trace of a matrix In Exercises 63-66, find the...Ch. 2.1 - Prob. 65E Ch. 2.1 - Prob. 66E Ch. 2.1 - Proof Prove that each statement is true when A and...Ch. 2.1 - Proof Prove that if A and B are square matrices of...Ch. 2.1 - Find conditions on w,x,y,andz such that AB=BA for...Ch. 2.1 - Prob. 70E Ch. 2.1 - Prob. 71E Ch. 2.1 - Show that no 22 matrices A and B exist that...Ch. 2.1 - Prob. 73E Ch. 2.1 - Prob. 74E Ch. 2.1 - Prob. 75E Ch. 2.1 - Prob. 76E Ch. 2.1 - Prob. 77E Ch. 2.1 - Prob. 78E Ch. 2.1 - Agriculture A fruit grower raises two crops,...Ch. 2.1 - Prob. 80E Ch. 2.1 - Prob. 81E Ch. 2.1 - Prob. 82E Ch. 2.1 - Prob. 83E Ch. 2.1 - Prob. 84E Ch. 2.1 - True or False? In Exercises 85 and 86, determine...Ch. 2.1 - True or False In Exercises 85 and 86, determine...Ch. 2.1 - Prob. 87E Ch. 2.2 - Evaluating an Expression In Exercise 1-6, evaluate...Ch. 2.2 - Evaluating an Expression In Exercise 1-6, evaluate...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Evaluating an Expression In Exercise 1-6, evaluate...Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Operations with Matrices In Exercises 7-12,...Ch. 2.2 - Prob. 10E Ch. 2.2 - Operations with Matrices In Exercises 7-12,...Ch. 2.2 - Prob. 12E Ch. 2.2 - Solve for X in the Equation, given A=-401-532 and...Ch. 2.2 - Solve for X in the Equation, given A=-2-1103-4 and...Ch. 2.2 - Operations with Matrices In Exercises 15-22,...Ch. 2.2 - Prob. 16E Ch. 2.2 - Operations with Matrices In Exercises 15-22,...Ch. 2.2 - Prob. 18E Ch. 2.2 - Operations with Matrices In Exercises 15-22,...Ch. 2.2 - Prob. 20E Ch. 2.2 - Prob. 21E Ch. 2.2 - Operations with Matrices In Exercises 15-22,...Ch. 2.2 - Associativity of Matrix Multiplication In...Ch. 2.2 - 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Multiplication with the Transpose of a Matrix In...Ch. 2.2 - Prob. 47E Ch. 2.2 - Prob. 48E Ch. 2.2 - Prob. 49E Ch. 2.2 - Prob. 50E Ch. 2.2 - Prob. 51E Ch. 2.2 - Prob. 52E Ch. 2.2 - Finding an nth Root of a Matrix In Exercises 53...Ch. 2.2 - Finding an nth Root of a Matrix In Exercises 53...Ch. 2.2 - Prob. 55E Ch. 2.2 - Prob. 56E Ch. 2.2 - Prob. 57E Ch. 2.2 - CAPSTONE In the matrix equation aX+AbB=bAB+IB...Ch. 2.2 - Polynomial Function In Exercises 59 and 60, find...Ch. 2.2 - Polynomial Function In Exercises 59 and 60, find...Ch. 2.2 - Guided proof Prove the associative property of...Ch. 2.2 - Proof Prove the associative property of...Ch. 2.2 - Proof Prove that the scalar 1 is the identity for...Ch. 2.2 - Proof Prove the distributive property: c+dA=cA+dA.Ch. 2.2 - Prob. 65E Ch. 2.2 - Prob. 66E Ch. 2.2 - Prob. 67E Ch. 2.2 - Proof Prove properties 2, 3, and 4 of Theorem 2.6.Ch. 2.2 - GuidedProof Prove that if A is an mn matrix, then...Ch. 2.2 - Prob. 70E Ch. 2.2 - Prob. 71E Ch. 2.2 - Symmetric and Skew-Symmetric Matrices In Exercises...Ch. 2.2 - Prob. 73E Ch. 2.2 - Prob. 74E Ch. 2.2 - Proof Prove that the main diagonal of a...Ch. 2.2 - Proof Prove that if A and B are nn skew-symmetric...Ch. 2.2 - Proof Let A be a square matrix of order n. a Show...Ch. 2.2 - Proof Prove that if A is an nn matrix, then A-AT...Ch. 2.2 - Prob. 79E Ch. 2.3 - The Inverse of a Matrix In Exercises 1-6, show...Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - The Inverse of a Matrix In Exercises 1-6, show...Ch. 2.3 - The Inverse of a Matrix In Exercises 1-6, show...Ch. 2.3 - Prob. 6E Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Prob. 8E Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Prob. 10E Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 2.3 - Prob. 17E Ch. 2.3 - Prob. 18E Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Prob. 24E Ch. 2.3 - Prob. 25E Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - Finding the Inverse of a Matrix In Exercises 7-30,...Ch. 2.3 - Prob. 29E Ch. 2.3 - Prob. 30E Ch. 2.3 - Finding the Inverse of a 22 Matrix In Exercises...Ch. 2.3 - Finding the Inverse of a 22 Matrix In Exercises...Ch. 2.3 - Prob. 33E Ch. 2.3 - Finding the Inverse of a 22 Matrix In Exercises...Ch. 2.3 - Finding the Inverse of a 22 Matrix In Exercises...Ch. 2.3 - Finding the Inverse of a 22 Matrix In Exercises...Ch. 2.3 - Prob. 37E Ch. 2.3 - Prob. 38E Ch. 2.3 - Finding the Inverse of the Square of a Matrix In...Ch. 2.3 - Finding the Inverse of the Square of a Matrix In...Ch. 2.3 - Finding the Inverses of Products and Transposes In...Ch. 2.3 - Finding the Inverses of Products and Transposes In...Ch. 2.3 - Finding the Inverses of Products and Transposes In...Ch. 2.3 - Prob. 44E Ch. 2.3 - Solving a System of Equations Using an Inverse In...Ch. 2.3 - Prob. 46E Ch. 2.3 - Solving a System of Equations Using an Inverse In...Ch. 2.3 - Solving a System of Equations Using an Inverse In...Ch. 2.3 - Prob. 49E Ch. 2.3 - Prob. 50E Ch. 2.3 - Prob. 51E Ch. 2.3 - Prob. 52E Ch. 2.3 - Matrix Equal to Its Own Inverse In Exercises 53...Ch. 2.3 - Matrix Equal to Its Own Inverse In Exercises 53...Ch. 2.3 - Singular Matrix In Exercises 55 and 56, find x...Ch. 2.3 - Singular Matrix In Exercises 55 and 56, find x...Ch. 2.3 - Prob. 57E Ch. 2.3 - Prob. 58E Ch. 2.3 - Prob. 59E Ch. 2.3 - Prob. 60E Ch. 2.3 - Prob. 61E Ch. 2.3 - Prob. 62E Ch. 2.3 - Prob. 63E Ch. 2.3 - Prob. 64E Ch. 2.3 - Prob. 65E Ch. 2.3 - Proof Prove that if A2=A, then I-2A=I-2A-1.Ch. 2.3 - Guided Proof Prove that the inverse of a symmetric...Ch. 2.3 - Prob. 68E Ch. 2.3 - Prob. 69E Ch. 2.3 - Prob. 70E Ch. 2.3 - Prob. 71E Ch. 2.3 - True or False ? 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Prove that if...Ch. 2.4 - CAPSTONE a Explain how to find an elementary...Ch. 2.4 - Show that the matrix below does not have an LU...Ch. 2.5 - Stochastic Matrices In Exercise 1-6, determine...Ch. 2.5 - Prob. 2E Ch. 2.5 - Prob. 3E Ch. 2.5 - Stochastic Matrices In Exercise 1-6, determine...Ch. 2.5 - Prob. 5E Ch. 2.5 - Prob. 6E Ch. 2.5 - Airplane Allocation An airline has 30 airplane in...Ch. 2.5 - Chemistry In a chemistry experiment, a test tube...Ch. 2.5 - Finding State Matrices In exercises 9 and 10, use...Ch. 2.5 - Finding State Matrices In exercises 9 and 10, use...Ch. 2.5 - Purchase of a product The market research...Ch. 2.5 - Spread of a Virus A medical researcher is studying...Ch. 2.5 - Prob. 13E Ch. 2.5 - Prob. 14E Ch. 2.5 - Smokers and Non smokers In a population of 10,000,...Ch. 2.5 - Consumer Preference In a population of 100,000...Ch. 2.5 - Regular and Steady State Matrices In Exercises...Ch. 2.5 - Prob. 18E Ch. 2.5 - Regular and Steady State Matrices In Exercises...Ch. 2.5 - 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Prob. 31CR Ch. 2.CR - Prob. 32CR Ch. 2.CR - Finding a Sequence of Elementary Matrix In...Ch. 2.CR - Prob. 34CR Ch. 2.CR - Prob. 35CR Ch. 2.CR - Finding a Sequence of Elementary Matrix In...Ch. 2.CR - Prob. 37CR Ch. 2.CR - Prob. 38CR Ch. 2.CR - Prob. 39CR Ch. 2.CR - Prob. 40CR Ch. 2.CR - Consider the matrices below....Ch. 2.CR - Prob. 42CR Ch. 2.CR - Prob. 43CR Ch. 2.CR - Prob. 44CR Ch. 2.CR - Prob. 45CR Ch. 2.CR - Prob. 46CR Ch. 2.CR - Solving a Linear System Using LU-Factorization In...Ch. 2.CR - Prob. 48CR Ch. 2.CR - Manufacturing A company manufactures tables and...Ch. 2.CR - Prob. 50CR Ch. 2.CR - Gasoline Sales Matrix A shows the numbers of...Ch. 2.CR - Prob. 52CR Ch. 2.CR - Prob. 53CR Ch. 2.CR - Prob. 54CR Ch. 2.CR - Prob. 55CR Ch. 2.CR - Prob. 56CR Ch. 2.CR - Prob. 57CR Ch. 2.CR - Prob. 58CR Ch. 2.CR - Finding State Matrices In Exercises 5962, use the...Ch. 2.CR - Prob. 60CR Ch. 2.CR - Prob. 61CR Ch. 2.CR - Prob. 62CR Ch. 2.CR - Prob. 63CR Ch. 2.CR - Prob. 64CR Ch. 2.CR - Prob. 65CR Ch. 2.CR - Regular and Steady State Matrix In Exercises 6568,...Ch. 2.CR - Regular and Steady State Matrix In Exercises 6568,...Ch. 2.CR - Prob. 68CR Ch. 2.CR - Prob. 69CR Ch. 2.CR - Classified Documents A courtroom has 2000...Ch. 2.CR - Prob. 71CR Ch. 2.CR - Prob. 72CR Ch. 2.CR - True or False? In Exercises 7376, determine...Ch. 2.CR - Prob. 74CR Ch. 2.CR - Prob. 75CR Ch. 2.CR - Prob. 76CR Ch. 2.CR - Encoding a Message In Exercises 77and 78, write...Ch. 2.CR - Encoding a Message In Exercises 77and 78, write...Ch. 2.CR - Decoding a Message In Exercises 79-82, use A1 to...Ch. 2.CR - Decoding a Message In Exercises 79-82, use A1 to...Ch. 2.CR - Decoding a Message In Exercises 79-82, use A1 to...Ch. 2.CR - Prob. 82CR Ch. 2.CR - Industrial System An industrial system has two...Ch. 2.CR - Prob. 84CR Ch. 2.CR - Prob. 85CR Ch. 2.CR - Prob. 86CR Ch. 2.CR - Prob. 87CR Ch. 2.CR - Prob. 88CR Ch. 2.CR - Cellular Phone Subscribers The table shows the...Ch. 2.CR - Prob. 90CR

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