Questions 1-12 are about the rules for determinants.
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Table of Contents
1.1
Vectors and Linear Combinations
1.2
Lengths and Dot Products
1.3
Matrices
2.1
Solving Linear Equations
2.2
The Idea of Elimination
2.3
Elimination Using Matrices
2.4
Rules for Matrix Operations
2.5
Inverse Matrices
2.6
Elimination = Factorization: A = L U
2.7
Transposes and Permutations
3.1
Spaces of Vectors
3.2
The Nullspace of A: Solving Ax = 0
3.3
The Rank and the Row Reduced Form
3.4
The Complete Solution to Ax = b
3.5
Independence, Basis and Dimension
3.6
Dimensions of the Four Subspaces
4.1
Orthogonality of the Four Subspaces
4.2
Projections
4.3
Least Squares Approximations
4.4
Orthogonal Bases and Gram-Schmidt
5.1
The Properties of Determinants
5.2
Permutations and Cofactors
5.3
Cramer's Rule, Inverses, and Volumes
6.1
Introduction to Eigenvalues
6.2
Diagonalizing a Matrix
6.3
Applications to Differential Equations
6.4
Symmetric Matrices
6.5
Positive Definite Matrices
6.6
Similar Matrices
6.7
Singular Value Decomposition (SVD)
7.1
The Idea of a Linear Transformation
7.2
The Matrix of a Linear Transformation
7.3
Diagonalization and the Pseudoinverse
8.1
Matrices in Engineering
8.2
Graphs and Networks
8.3
Markov Matrices, Population, and Economics
8.4
Linear Programming
8.5
Fourier Series: Linear Algebra for Functions
8.6
Linear Algebra for Statistics and Probability
8.7
Computer Graphics
9.1
Gaussian Elimination in Practice
9.2
Norms and Condition Numbers
9.3
Iterative Methods and Preconditioners
10.1
Complex Numbers
10.2
Hermitian and Unitary Matrices
10.3
The Fast Fourier Transform
Textbook Solutions for Introduction to Linear Algebra
Chapter 5.1 Problem 1
Question
Questions are about Markov matrices and their eigenvalues and powers.
Find the eigenvalues of this Markov matrix (their sum is the trace):
\(A=\left[\begin{array}{ll}
.90 & .15 \\
.10 & .85
\end{array}\right]\)
What is the steady state eigenvector for the eigenvalue \(\lambda_{1}=1\)?
Solution
The first step in solving 5.1 problem number 1 trying to solve the problem we have to refer to the textbook question: Questions are about Markov matrices and their eigenvalues and powers.Find the eigenvalues of this Markov matrix (their sum is the trace):\(A=\left[\begin{array}{ll}.90 & .15 \\.10 & .85\end{array}\right]\)What is the steady state eigenvector for the eigenvalue \(\lambda_{1}=1\)?
From the textbook chapter The Properties of Determinants you will find a few key concepts needed to solve this.
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full solution
full solution
Title
Introduction to Linear Algebra 4
Author
Gilbert Strang
ISBN
9780980232714
Get solution: Questions 1-12 are about the rules for determinants
Chapter 5.1 textbook questions
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Chapter 5: Problem 1 Introduction to Linear Algebra 4
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Chapter 5: Problem 2 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 3 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 4 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 5 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 6 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 7 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 8 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 9 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 10 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 11 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 12 Introduction to Linear Algebra 4
Questions 1-12 are about the rules for determinants.
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Chapter 5: Problem 13 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 14 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 15 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 16 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 17 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 18 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 19 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 20 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 21 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 22 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 23 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 24 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 25 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 26 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 27 Introduction to Linear Algebra 4
Questions 13-27 use the rules to compute specific determinants.
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Chapter 5: Problem 28 Introduction to Linear Algebra 4
True or false (give a reason if true or a 2 by 2 example if false): (a) If A is not invertible then AB is not invertible. (b) The determinant of A is always the product of its pivots. (c) The determinant of A - B equals det A - det B. (d) AB and BA have the same determinant.
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Chapter 5: Problem 29 Introduction to Linear Algebra 4
What is wrong with this proof that projection matrices have det P = I? P = A(AT A)-I AT so IP I = IAIIAT~IAIIATI = 1.
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Chapter 5: Problem 30 Introduction to Linear Algebra 4
(Calculus question) Show that the partial derivatives ofln(detA) give A-I! ~l j(a, b, e, d) = In(ad - be) leads to [aj/aa aj/ae] - A
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Chapter 5: Problem 31 Introduction to Linear Algebra 4
(MATLAB) The Hilbert matrix hilb(n) has i, j entry equal to 1/0 + j - 1). Print the determinants of hilb(1), hilb(2), ... , hilb(10). Hilbert matrices are hard to work with! What are the pivots of hilb (5)?
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Chapter 5: Problem 32 Introduction to Linear Algebra 4
(MATLAB) What is a typical determinant (experimentally) of rand(n) and randn(n) for n = 50, 100,200, 400? (And what does "Inf" mean in MATLAB?)
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Chapter 5: Problem 33 Introduction to Linear Algebra 4
(MATLAB) Find the largest determinant of a 6 by 6 matrix of 1 's and -1 'so
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Chapter 5: Problem 34 Introduction to Linear Algebra 4
If you know that det A = 6, what is the determinant of B? row 1 row 3 + row 2 + row 1 From det A = row 2 = 6 find det B = row 2 + row 1 row 3 row 1
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