1 Systems Of Linear Equations 2 Matrices 3 Determinants 4 Vector Spaces 5 Inner Product Spaces 6 Linear Transformations 7 Eigenvalues And Eigenvectors A Appendix Chapter3: Determinants
3.1 The Determinants Of A Matrix 3.2 Determininants And Elementary Operations 3.3 Properties Of Determinants 3.4 Applications Of Determinants 3.CR Review Exercises 3.CM Cumulative Review Section3.3: Properties Of Determinants
Problem 1E: The determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then... Problem 2E: The determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then... Problem 3E: The determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then... Problem 4E: The determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|. Then... Problem 5E: The determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then... Problem 6E Problem 7E: The Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to... Problem 8E Problem 9E: The Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to... Problem 10E Problem 11E: The Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to... Problem 12E: The Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to... Problem 13E: The Determinant of a scalar multiple of a Matrix In Exercises 7-14, use the fact that |cA|=cn|A| to... Problem 14E Problem 15E: The Determinant of a Matrix Sum In Exercises 15-18, find (a)|A|,(b)|B|,(c)A+B and (d)|A+B|. Then... Problem 16E Problem 17E: The Determinant of a Matrix Sum In Exercises 15-18, find (a)|A|,(b)|B|,(c)A+Band(d)|A+B|.Then verify... Problem 18E Problem 19E: Classifying Matrices as Singular or Nonsingular In Exercises 19-24, use a determinant to decide... Problem 20E Problem 21E: Classifying Matrices as Singular or Nonsingular In Exercises 19-24, use a determinant to decide... Problem 22E: Classifying Matrices as Singular or Nonsingular In Exercises 19-24, use a determinant to decide... Problem 23E: Classifying Matrices as Singular or Nonsingular In Exercises 19-24, use a determinant to decide... Problem 24E Problem 25E: The Determinant of a Matrix in Exercises 25-30, find |A1|.Being by finding A1, and then evaluate its... Problem 26E: The Determinant of a Matrix in Exercises 25-30, find |A1|.Being by finding A1, and then evaluate its... Problem 27E: The Determinant of a Matrix in Exercises 25-30, find |A1|.Being by finding A1, and then evaluate its... Problem 28E: The Determinant of a Matrix in Exercises 25-30, find |A1|.Being by finding A1, and then evaluate its... Problem 29E: The Determinant of a Matrix in Exercises 25-30, find |A1|.Being by finding A1, and then evaluate its... Problem 30E Problem 31E: System of Linear Equation In Exercises 31-36, use the determinant of the coefficient matrix to... Problem 32E: System of Linear Equation In Exercises 31-36, use the determinant of the coefficient matrix to... Problem 33E: System of Linear Equation In Exercises 31-36, use the determinant of the coefficient matrix to... Problem 34E: System of Linear Equation In Exercises 31-36, use the determinant of the coefficient matrix to... Problem 35E Problem 36E Problem 37E: Singular Matrices In Exercises 37-42, find the values of ksuch that Ais singular. A=[k132k2] Problem 38E: Singular Matrices In Exercises 37-42, find the values of ksuch that Ais singular. A=[k122k+2] Problem 39E: Singular Matrices In Exercises 37-42, find the values of ksuch that Ais singular. A=[10301042k] Problem 40E: Singular Matrices In Exercises 37-42, find the values of ksuch that Ais singular. A=[1k220k314] Problem 41E: Singular Matrices In Exercises 37-42, find the values of k such that A is singular. A=[0k1k1k1k0] Problem 42E Problem 43E: Finding Determinants In Exercises 43-50, find (a)|AT|,(b)|A2|,(c)|AAT|,(d)|2A|, and (e)|A1|.... Problem 44E Problem 45E: Finding Determinants In Exercises 43-50, find (a)|AT|,(b)|A2|,(c)|AAT|,(d)|2A|, and (e)|A1|.... Problem 46E Problem 47E: Finding Determinants In Exercises 43-50, find (a)|AT|,(b)|A2|,(c)|AAT|,(d)|2A|, and (e)|A1|.... Problem 48E Problem 49E: Finding Determinants In Exercises 43-50, find (a)|AT|,(b)|A2|,(c)|AAT|,(d)|2A|, and (e)|A1|.... Problem 50E Problem 51E: Finding Determinants In Exercises 51-56, use a software program or a graphing utility to find a |A|,... Problem 52E Problem 53E Problem 54E Problem 55E Problem 56E Problem 57E: Let A and B be square matrices of order 4 such that |A|=5 and |B|=3.Find a |A2|, b |B2|, c |A3|, and... Problem 58E: CAPSTONE Let A and B be square matrices of order 3 such that |A|=4 and |B|=5. a Find |AB| b Find... Problem 59E: Proof Let A and B be nn matrices such that AB=I.Prove that |A|0 and |B|0. Problem 60E Problem 61E: Find two 22 matrices such that |A|+|B|=|A+B|. Problem 62E Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|. Problem 64E: Illustrate the result of Exercise 63 with the matrix A=[211312022] Problem 65E: Guided Proof Prove that the determinant of an invertible matrix A is equal to 1 when all of the... Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E Problem 76E: Orthogonal Matrices in Exercises 73-78, determine whether the matrix is orthogonal. An invertible... Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E Problem 83E: Proof If A is an idempotent matrix (A2=A), then prove that the determinant of A is either 0 or 1. Problem 84E Problem 63E: Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
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