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Math Algebra Elementary Linear Algebra (MindTap Course List)

Finding the Determinant of a Triangular Matrix In Exercises 39-42, find the determinant of the triangular matrix. [ − 2 0 0 4 6 0 − 3 7 2 ]

Finding the Determinant of a Triangular Matrix In Exercises 39-42, find the determinant of the triangular matrix. [ − 2 0 0 4 6 0 − 3 7 2 ]

Solution Summary: The author explains that if A is a triangular matrix of order n, its determinant is the product of the entries on the main diagonal.

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN: 9781305658004

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 3.1, Problem 39E

Finding the Determinant of a Triangular Matrix In Exercises 39-42, find the determinant of the triangular matrix.

[ − 2 0 0 4 6 0 − 3 7 2 ]

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Chapter 3.1, Problem 38E

Chapter 3.1, Problem 40E

Chapter 3 Solutions

Elementary Linear Algebra (MindTap Course List)

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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