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Math Algebra Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

(a) To find: Whether the given statement “Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant” is true or false.

(a) To find: Whether the given statement “Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant” is true or false.

Solution Summary: The author explains that two matrices are column equivalent if one can be changed to the other by a sequence of elementary column operations.

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

8th Edition

ISBN: 9781337604925

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 3.2, Problem 38E

To determine

(a)

To find:

Whether the given statement “Adding a multiple of one column of a square matrix to another column changes only the sign of the determinant” is true or false.

To determine

(b)

To find:

Whether the given statement “Two matrices are column-equivalent when one matrix can be obtained by performing elementary column operations on the other” is true or false.

To determine

(c)

To find:

Whether the given statement “If one row of a square matrix is a multiple of another row, then the determinant is 0” is true or false.

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Chapter 3.2, Problem 37E

Chapter 3.2, Problem 39E

Chapter 3 Solutions

Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term

Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - The Determinant of a Matrix In Exercises 1-12,...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Finding the Minors and Cofactors of a Matrix In...Ch. 3.1 - Find the determinant of the matrix in Exercise 15...Ch. 3.1 - Find the determinant of the matrix in Exercise 16...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Prob. 24E Ch. 3.1 - Find a Determinant In Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Finding a determinant in Exercises 19-32, use...Ch. 3.1 - Prob. 32E Ch. 3.1 - Finding a Determinant in Exercises 33 and 34, use...Ch. 3.1 - Finding a Determinant in Exercises 33 and 34, use...Ch. 3.1 - Finding a Determinant In Exercises 35-38, use a...Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - Finding the Determinant of a Triangular Matrix In...Ch. 3.1 - True or False ? a The determinant of a 22 matrix A...Ch. 3.1 - True or False ? a To find the determinant of a...Ch. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Prob. 46E Ch. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Solving an Equation In Exercises 45-48, solve for...Ch. 3.1 - Solving an Equation In Exercises 4952, find the...Ch. 3.1 - Solving an Equation In Exercises 4952, find the...Ch. 3.1 - Solving an Equation In Exercises 49-52, find the...Ch. 3.1 - Solving an Equation In Exercises 49-52, find the...Ch. 3.1 - Show that the system of linear equations...Ch. 3.1 - Prob. 54E Ch. 3.1 - Entries Involving Expressions In Exercises 55- 62,...Ch. 3.1 - Prob. 56E Ch. 3.1 - Entries Involving Expressions In Exercises 55-62,...Ch. 3.1 - Prob. 58E Ch. 3.1 - Entries Involving Expressions In Exercises 55- 62,...Ch. 3.1 - Prob. 60E Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Verifying an Equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 64E Ch. 3.1 - Verify an Equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 66E Ch. 3.1 - Verifying an equation In Exercises 63-68, evaluate...Ch. 3.1 - Prob. 68E Ch. 3.1 - You are given the equation |x0c1xb01a|=ax2+bx+c....Ch. 3.1 - The determinant of a 22 matrix involves two...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 6E Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 8E Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 10E Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 12E Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 16E Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Prob. 18E Ch. 3.2 - Properties of Determinant In Exercises 1-20,...Ch. 3.2 - Properties of Determinants In Exercises 1-20,...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Finding a Determinant In Exercises 2124, use...Ch. 3.2 - Prob. 24E Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 26E Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 28E Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 34E Ch. 3.2 - Finding a Determinant In Exercises 25-36, use...Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Finding the Determinant of an Elementary Matrix In...Ch. 3.2 - Proof Prove the property....Ch. 3.2 - Proof Prove the property....Ch. 3.2 - Find each determinant. a |cossinsincos| b...Ch. 3.2 - CAPSTONE Evaluate each determinant when a = 1, b =...Ch. 3.2 - Guided Proof Prove Property 2 of Theorem 3.3: When...Ch. 3.2 - Prob. 48E Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - The determinant of a matrix product In Exercises...Ch. 3.3 - Prob. 6E Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 8E Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 10E Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - The Determinant of a scalar multiple of a Matrix...Ch. 3.3 - Prob. 14E Ch. 3.3 - The Determinant of a Matrix Sum In Exercises...Ch. 3.3 - Prob. 16E Ch. 3.3 - The Determinant of a Matrix Sum In Exercises...Ch. 3.3 - Prob. 18E Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Prob. 20E Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Classifying Matrices as Singular or Nonsingular In...Ch. 3.3 - Prob. 24E Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - The Determinant of a Matrix in Exercises 25-30,...Ch. 3.3 - Prob. 30E Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - System of Linear Equation In Exercises 31-36, use...Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Singular Matrices In Exercises 37-42, find the...Ch. 3.3 - Prob. 42E Ch. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 44E Ch. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 46E Ch. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 48E Ch. 3.3 - Finding Determinants In Exercises 43-50, find...Ch. 3.3 - Prob. 50E Ch. 3.3 - Finding Determinants In Exercises 51-56, use a...Ch. 3.3 - Prob. 52E Ch. 3.3 - Prob. 53E Ch. 3.3 - Prob. 54E Ch. 3.3 - Prob. 55E Ch. 3.3 - Prob. 56E Ch. 3.3 - Let A and B be square matrices of order 4 such...Ch. 3.3 - CAPSTONE Let A and B be square matrices of order 3...Ch. 3.3 - Proof Let A and B be nn matrices such that...Ch. 3.3 - Prob. 60E Ch. 3.3 - Find two 22 matrices such that |A|+|B|=|A+B|.Ch. 3.3 - Prob. 62E Ch. 3.3 - Let A be an nn matrix in which the entries of each...Ch. 3.3 - Illustrate the result of Exercise 63 with the...Ch. 3.3 - Guided Proof Prove that the determinant of an...Ch. 3.3 - Prob. 66E Ch. 3.3 - Prob. 67E Ch. 3.3 - Prob. 68E Ch. 3.3 - Prob. 69E Ch. 3.3 - Prob. 70E Ch. 3.3 - Prob. 71E Ch. 3.3 - Prob. 72E Ch. 3.3 - Prob. 73E Ch. 3.3 - Prob. 74E Ch. 3.3 - Prob. 75E Ch. 3.3 - Orthogonal Matrices in Exercises 73-78, determine...Ch. 3.3 - Prob. 77E Ch. 3.3 - Prob. 78E Ch. 3.3 - Prob. 79E Ch. 3.3 - Prob. 80E Ch. 3.3 - Prob. 81E Ch. 3.3 - Prob. 82E Ch. 3.3 - Proof If A is an idempotent matrix (A2=A), then...Ch. 3.3 - Prob. 84E Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Prob. 2E Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Prob. 6E Ch. 3.4 - Prob. 7E Ch. 3.4 - Finding the Adjoint and Inverse of a Matrix In...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 10E Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - Prob. 15E Ch. 3.4 - Prob. 16E Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 20E Ch. 3.4 - Using Cramers Rule In Exercises 9-22, use Cramers...Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Use Cramers Rule to solve the system of linear...Ch. 3.4 - Verify the system of linear equations in cosA,...Ch. 3.4 - Finding the Area of a Triangle In Exercises 29-32,...Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Finding an Equation of a Line In Exercises 37-40,...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Finding the Volume of a Tetrahedron In Exercises...Ch. 3.4 - Testing for Coplanar Points In Exercises 47-52,...Ch. 3.4 - Testing for Coplanar Points In Exercises 47-52,...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Testing for Coplanar Points In exercises 47-52...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Finding an equation of a plane In Exercises 53-58,...Ch. 3.4 - Using Cramers Rule In Exercises 59 and 60,...Ch. 3.4 - Using Cramers Rule In Exercises 59 and 60,...Ch. 3.4 - Software Publishing The table shows the estimate...Ch. 3.4 - Prob. 62E Ch. 3.4 - Prob. 63E Ch. 3.4 - Prob. 64E Ch. 3.4 - Prob. 65E Ch. 3.4 - Prob. 66E Ch. 3.4 - Prob. 67E Ch. 3.4 - Prob. 68E Ch. 3.4 - Prob. 69E Ch. 3.4 - Prob. 70E Ch. 3.CR - The Determinant of a Matrix In Exercises 1-18,...Ch. 3.CR - Prob. 2CR Ch. 3.CR - Prob. 3CR Ch. 3.CR - Prob. 4CR Ch. 3.CR - Prob. 5CR Ch. 3.CR - Prob. 6CR Ch. 3.CR - Prob. 7CR Ch. 3.CR - Prob. 8CR Ch. 3.CR - Prob. 9CR Ch. 3.CR - The Determinant of a Matrix In Exercises 1-18,...Ch. 3.CR - Prob. 11CR Ch. 3.CR - Prob. 12CR Ch. 3.CR - Prob. 13CR Ch. 3.CR - Prob. 14CR Ch. 3.CR - Prob. 15CR Ch. 3.CR - Prob. 16CR Ch. 3.CR - Prob. 17CR Ch. 3.CR - Prob. 18CR Ch. 3.CR - Properties of Determinants In Exercises 19-22,...Ch. 3.CR - Properties of Determinants In Exercises 19-22,...Ch. 3.CR - Prob. 21CR Ch. 3.CR - Prob. 22CR Ch. 3.CR - Prob. 23CR Ch. 3.CR - Prob. 24CR Ch. 3.CR - Prob. 25CR Ch. 3.CR - Prob. 26CR Ch. 3.CR - Prob. 27CR Ch. 3.CR - Finding Determinants In Exercises 27 and 28, find...Ch. 3.CR - Prob. 29CR Ch. 3.CR - Prob. 30CR Ch. 3.CR - Prob. 31CR Ch. 3.CR - The Determinant of the Inverse of a Matrix In...Ch. 3.CR - Prob. 33CR Ch. 3.CR - Prob. 34CR Ch. 3.CR - Solving a System of Linear Equations In Exercises...Ch. 3.CR - Solving a System of Linear Equations In Exercises...Ch. 3.CR - Prob. 37CR Ch. 3.CR - Prob. 38CR Ch. 3.CR - System of Linear Equation In Exercises 37-42, use...Ch. 3.CR - System of Linear Equation In Exercises 37-42, use...Ch. 3.CR - Prob. 41CR Ch. 3.CR - Prob. 42CR Ch. 3.CR - Let A and B be square matrices of order 4 such...Ch. 3.CR - Prob. 44CR Ch. 3.CR - Prob. 45CR Ch. 3.CR - Prob. 46CR Ch. 3.CR - Prob. 47CR Ch. 3.CR - Show that |a1111a1111a1111a|=(a+3)(a1)3 Ch. 3.CR - Prob. 49CR Ch. 3.CR - Prob. 50CR Ch. 3.CR - Prob. 51CR Ch. 3.CR - Prob. 52CR Ch. 3.CR - Prob. 53CR Ch. 3.CR - Prob. 54CR Ch. 3.CR - Prob. 55CR Ch. 3.CR - Prob. 56CR Ch. 3.CR - Prob. 57CR Ch. 3.CR - Prob. 58CR Ch. 3.CR - Prob. 59CR Ch. 3.CR - Prob. 60CR Ch. 3.CR - Prob. 61CR Ch. 3.CR - Prob. 62CR Ch. 3.CR - Prob. 63CR Ch. 3.CR - Prob. 64CR Ch. 3.CR - Prob. 65CR Ch. 3.CR - Using Cramers Rule In Exercises 65 and 66, use a...Ch. 3.CR - Prob. 67CR Ch. 3.CR - Prob. 68CR Ch. 3.CR - Prob. 69CR Ch. 3.CR - Prob. 70CR Ch. 3.CR - Prob. 71CR Ch. 3.CR - Prob. 72CR Ch. 3.CR - Prob. 73CR Ch. 3.CR - Health Care Expenditures The table shows annual...Ch. 3.CR - Prob. 75CR Ch. 3.CR - Prob. 76CR Ch. 3.CR - True or False? In Exercises 75-78, determine...Ch. 3.CR - Prob. 78CR Ch. 3.CM - Prob. 1CM Ch. 3.CM - Prob. 2CM Ch. 3.CM - In Exercises 3and4, use Gaussian elimination to...Ch. 3.CM - In Exercises 3and4, use Gaussian elimination to...Ch. 3.CM - Use a software program or a graphing utility to...Ch. 3.CM - Prob. 6CM Ch. 3.CM - Solve the homogeneous linear system corresponding...Ch. 3.CM - Determine the values of k such that the system is...Ch. 3.CM - Solve for x and y in the matrix equation 2AB=I,...Ch. 3.CM - Find ATA for the matrix A=[531246]. Show that this...Ch. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - Prob. 13CM Ch. 3.CM - In Exercises 11-14, find the inverse of the matrix...Ch. 3.CM - In Exercises 15 and 16, use an inverse matrix to...Ch. 3.CM - In Exercises 15 and 16, use an inverse matrix to...Ch. 3.CM - Find the sequence of the elementary matrices whose...Ch. 3.CM - Find the determinant of the matrix....Ch. 3.CM - Find a |A|, b |B|, c AB and d |AB| then verify...Ch. 3.CM - Find a |A| and b |A1| A=[523104682]Ch. 3.CM - If |A|=7 and A is of order 4. Then find each...Ch. 3.CM - Use the adjoint of A=[151021102] to find A1 Ch. 3.CM - Let X1,X2,X3 and b be the column matrices below....Ch. 3.CM - Use a system of linear equation to find the...Ch. 3.CM - Use a determinant to find an equation of the line...Ch. 3.CM - Use a determinant to find the area of the triangle...Ch. 3.CM - Determine the currents I1I2 and I3 for the...Ch. 3.CM - A manufacture produce three models of a product...Ch. 3.CM - Prob. 29CM

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