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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Chapter 7.CM, Problem 10CM
To determine
To find:
The standard matrix for the given linear transformation
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Assume there is the following simplified grade book:
Homework Labs | Final Exam | Project
Avery
95
98
90
100
Blake
90
96
Carlos
83
79
Dax
55
30
228
92
95
79
90
65
60
Assume that the weights used to compute the final grades are homework 0.3, labs 0.2,
the final 0.35, and the project 0.15.
| Write an explicit formula to compute Avery's final grade using a single
inner product.
Write an explicit formula to compute everyone's final grade simultane-
ously using a single matrix-vector product.
1. Explicitly compute by hand (with work shown) the following Frobenius inner
products
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4.56 3.12
(a) ((º º º). (156
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Chapter 7 Solutions
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term
Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and Eigenvectors in...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Verifying Eigenvalues and EigenvectorsIn Exercises...Ch. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...
Ch. 7.1 - Determining Eigenvectors In Exercise 9-12,...Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Prob. 18ECh. 7.1 - Characteristic Equation, Eigenvalues, and...Ch. 7.1 - Prob. 20ECh. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Prob. 24ECh. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Characteristic Equation, Eigenvalues and...Ch. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Finding EigenvaluesIn Exercises 29-40, use a...Ch. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Prob. 43ECh. 7.1 - Eigenvalues of Triangular and Diagonal Matrices In...Ch. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Prob. 46ECh. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Eigenvalues and Eigenvectors of Linear...Ch. 7.1 - Cayley-Hamilton TheoremIn Exercises 49-52,...Ch. 7.1 - Cayley-Hamilton TheoremIn Exercises 49-52,...Ch. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Proof Prove that A and AT have the same...Ch. 7.1 - Prob. 59ECh. 7.1 - Define T:R2R2 by T(v)=projuv Where u is a fixed...Ch. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Show that A=[0110] has no real eigenvalues.Ch. 7.1 - True or False? In Exercises 67 and 68, determine...Ch. 7.1 - True or False? In Exercises 67 and 68, determine...Ch. 7.1 - Finding the Dimension of an Eigenspace In...Ch. 7.1 - Finding the Dimension of an Eigenspace In...Ch. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Define T:P2P2 by...Ch. 7.1 - Prob. 77ECh. 7.1 - Find all values of the angle for which the matrix...Ch. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Diagonalizable Matrices and Eigenvalues In...Ch. 7.2 - Prob. 6ECh. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Prob. 8ECh. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Diagonalizing a Matrix In Exercise 7-14, find if...Ch. 7.2 - Prob. 14ECh. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Prob. 16ECh. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Show That a Matrix Is Not Diagonalizable In...Ch. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Determine a Sufficient Condition for...Ch. 7.2 - Finding a Basis In Exercises 27-30, find a basis B...Ch. 7.2 - Finding a Basis In Exercises 27-30, find a basis B...Ch. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Finding a Power of a Matrix In Exercises 33-36,...Ch. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - True or False? In Exercises 37 and 38, determine...Ch. 7.2 - True or False? In Exercises 37 and 38, determine...Ch. 7.2 - Are the two matrices similar? If so, find a matrix...Ch. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Proof Prove that if matrix A is diagonalizable,...Ch. 7.2 - Proof Prove that if matrix A is diagonalizable...Ch. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Guide Proof Prove nonzero nilpotent matrices are...Ch. 7.2 - Prob. 47ECh. 7.2 - CAPSTONE Explain how to determine whether an nn...Ch. 7.2 - Prob. 49ECh. 7.2 - Showing That a Matrix Is Not Diagonalizable In...Ch. 7.3 - Determining Whether a Matrix Is Symmetric In...Ch. 7.3 - Prob. 2ECh. 7.3 - Proof In Exercise 3-6, prove that the symmetric...Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Finding Eigenvalues and Dimensions of Eigen spaces...Ch. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Determine Whether a Matrix Is Orthogonal In...Ch. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Eigenvectors of Symmetric Matrix In Exercises...Ch. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Orthogonally Diagonalizable Matrices In Exercise...Ch. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 4-52, find...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Orthogonal Diagonalization In Exercise 43-52, find...Ch. 7.3 - Orthogonal Diagonalization In Exercise 4-52, find...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Find ATA and AAT for the matrix below. What do you...Ch. 7.4 - Finding Age Distribution Vectors In Exercises 1-6,...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Finding Age Distribution Vectors In Exercises 1-6,...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Population Growth Model A population has the...Ch. 7.4 - Population Growth Model A population has the...Ch. 7.4 - Prob. 9ECh. 7.4 - Find the limit if it exists of Anx1 as n...Ch. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 23ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Solving a System of Linear Differential Equations...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Rotation of a Conic In Exercises 45-52, use the...Ch. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Prob. 67ECh. 7.4 - Use your schools library, the Internet, or some...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Prob. 4CRCh. 7.CR - Characteristic Equation, Eigenvalues, and Basis In...Ch. 7.CR - Prob. 6CRCh. 7.CR - Characteristics Equation, Eigenvalues, and Basis...Ch. 7.CR - Characteristics Equation, Eigenvalues, and Basis...Ch. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 10CRCh. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 12CRCh. 7.CR - Determining Whether a Matrix Is DiagonalizableIn...Ch. 7.CR - Prob. 14CRCh. 7.CR - For what values of a does the matrix A=[01a1] have...Ch. 7.CR - Prob. 16CRCh. 7.CR - Writing In Exercises 17-20, explain why the given...Ch. 7.CR - Prob. 18CRCh. 7.CR - Writing In Exercises 17-20, explain why the given...Ch. 7.CR - Prob. 20CRCh. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determine Whether Two Matrices Are Similar In...Ch. 7.CR - Determining Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 26CRCh. 7.CR - Determining Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 28CRCh. 7.CR - Prob. 29CRCh. 7.CR - Determine Symmetric and Orthogonal Matrices In...Ch. 7.CR - Prob. 31CRCh. 7.CR - Prob. 32CRCh. 7.CR - Prob. 33CRCh. 7.CR - Prob. 34CRCh. 7.CR - Prob. 35CRCh. 7.CR - Prob. 36CRCh. 7.CR - Orthogonally Diagonalizable Matrices In Exercises...Ch. 7.CR - Prob. 38CRCh. 7.CR - Orthogonally Diagonalizable Matrices In Exercises...Ch. 7.CR - Prob. 40CRCh. 7.CR - Prob. 41CRCh. 7.CR - Prob. 42CRCh. 7.CR - Prob. 43CRCh. 7.CR - Prob. 44CRCh. 7.CR - Prob. 45CRCh. 7.CR - Orthogonal Diagonalization In Exercises 41-46,...Ch. 7.CR - Prob. 47CRCh. 7.CR - Prob. 48CRCh. 7.CR - Prob. 49CRCh. 7.CR - Prob. 50CRCh. 7.CR - Prob. 51CRCh. 7.CR - Prob. 52CRCh. 7.CR - Steady State Probability Vector In Exercises...Ch. 7.CR - Prob. 54CRCh. 7.CR - Prob. 55CRCh. 7.CR - Prob. 56CRCh. 7.CR - Prob. 57CRCh. 7.CR - Prob. 58CRCh. 7.CR - Prob. 59CRCh. 7.CR - Prob. 60CRCh. 7.CR - Prob. 61CRCh. 7.CR - Prob. 62CRCh. 7.CR - Prob. 63CRCh. 7.CR - a Find a symmetric matrix B such that B2=A for...Ch. 7.CR - Determine all nn symmetric matrices that have 0 as...Ch. 7.CR - Prob. 66CRCh. 7.CR - Prob. 67CRCh. 7.CR - Prob. 68CRCh. 7.CR - Prob. 69CRCh. 7.CR - True or False? In Exercises 69 and 70, determine...Ch. 7.CR - Prob. 71CRCh. 7.CR - Prob. 72CRCh. 7.CR - Prob. 73CRCh. 7.CR - Prob. 74CRCh. 7.CR - Prob. 75CRCh. 7.CR - Prob. 76CRCh. 7.CR - Prob. 77CRCh. 7.CR - Prob. 78CRCh. 7.CR - Prob. 79CRCh. 7.CR - Prob. 80CRCh. 7.CR - Prob. 81CRCh. 7.CR - Prob. 82CRCh. 7.CR - Prob. 83CRCh. 7.CR - Prob. 84CRCh. 7.CR - Prob. 85CRCh. 7.CR - Prob. 86CRCh. 7.CR - Prob. 87CRCh. 7.CR - Prob. 88CRCh. 7.CM - Prob. 1CMCh. 7.CM - In Exercises 1 and 2, determine whether the...Ch. 7.CM - Let T:RnRm be the linear transformation defined by...Ch. 7.CM - Prob. 4CMCh. 7.CM - Find the kernel of the linear transformation...Ch. 7.CM - Let T:R4R2 be the linear transformation defined by...Ch. 7.CM - In Exercises 7-10, find the standard matrix for...Ch. 7.CM - Prob. 8CMCh. 7.CM - Prob. 9CMCh. 7.CM - Prob. 10CMCh. 7.CM - Prob. 11CMCh. 7.CM - Prob. 12CMCh. 7.CM - Prob. 13CMCh. 7.CM - Prob. 14CMCh. 7.CM - Prob. 15CMCh. 7.CM - Prob. 16CMCh. 7.CM - Prob. 17CMCh. 7.CM - Prob. 18CMCh. 7.CM - In Exercises 19-22, find the eigenvalues and the...Ch. 7.CM - Prob. 20CMCh. 7.CM - Prob. 21CMCh. 7.CM - Prob. 22CMCh. 7.CM - In Exercises 23 and 24, find a nonsingular matrix...Ch. 7.CM - In Exercises 23 and 24, find a nonsingular matrix...Ch. 7.CM - Find a basis B for R3 such that the matrix for the...Ch. 7.CM - Find an orthogonal matrix P such that PTAP...Ch. 7.CM - Use the Gram-Schmidt orthonormalization process to...Ch. 7.CM - Prob. 28CMCh. 7.CM - Prob. 29CMCh. 7.CM - Prob. 30CMCh. 7.CM - Prob. 31CMCh. 7.CM - Prove that if A is similar to B and A is...
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