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|.
Related questions
a. What are the vectors that are part of the Col(A) and Col(AT )?
b. Determine the Null(AT ).
c. Determine the rank of the matrix A.
Transcribed Image Text: Given the matrix below and its corresponding rref(A) and rref(A')
1000
-2
-1 -3
(10000
0100
3
- 12 I
3
01000
A =
RREF (A) =
RREF (A") =
0 010
4
- 16 2
6
0 01 30
0 00 1
- 10
16
-3 -9 - I
0 00 0 1
0 000
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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