Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))

9th Edition

ISBN: 9780321962218

Author: Steven J. Leon

Publisher: PEARSON

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Textbook Question

Chapter 4, Problem 7CTB

Let L be the translation operator on ℝ 2 defined by
L ( x ) = x + a , where a = [ 2 5 ]
Find the matrix representation of L with respect to the homogeneous coordinate system.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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Chapter 4, Problem 6CTB

Chapter 4, Problem 8CTB

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Chapter 4 Solutions

Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))

Ch. 4.1 - Show that each of the following are linear...Ch. 4.1 - Let L be the linear operator on 2 defined by...Ch. 4.1 - Let a be a fixed nonzero vector in 2 . A mapping...Ch. 4.1 - Let L: 22 be a linear operator. If...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Let C be a fixed nn matrix. Determine whether the...Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - For each fC[0,1] , define L(f)=F , where F(x)= 0...

Ch. 4.1 - Determine whether the following are linear...Ch. 4.1 - Use mathematical induction to prove that if L is a...Ch. 4.1 - Let {v1,...,vn} be a basis for a vector space V,...Ch. 4.1 - Let L be a linear operator on 1 and let a=L(1) ....Ch. 4.1 - Let L be a linear operator on a vector space V....Ch. 4.1 - Let L1:UV and L2:VW be a linear transformations,...Ch. 4.1 - Determine the kernel and range of each of the...Ch. 4.1 - Let S be the subspace of 3 spanned by e1 and e2 ....Ch. 4.1 - Find the kernel and range of each of the following...Ch. 4.1 - Let L:VW be a linear transformation, and let T be...Ch. 4.1 - A linear transformation L:VW is said to be...Ch. 4.1 - A linear transformation L:VW is said to be map V...Ch. 4.1 - Which of the operators defined in Exercise 17 are...Ch. 4.1 - Let A be a 22 matrix, and let LA be the linear...Ch. 4.1 - Let D be the differentiation operator on P3 , and...Ch. 4.2 - Refer to Exercise 1 of Section 4.1. For each...Ch. 4.2 - For each of the following linear transformations L...Ch. 4.2 - For each of the following linear operators L on 3...Ch. 4.2 - Let L be the linear operators on 3 defined by...Ch. 4.2 - Find the standard matrix representation for each...Ch. 4.2 - Let b1=[110],b2=[101],b3=[011] and let L be the...Ch. 4.2 - Let y1=[111],y2=[110],y3=[100] and let I be the...Ch. 4.2 - Let y1,y2, and y3 be defined as in Exercise 7, and...Ch. 4.2 - Let R=[001100110011111] The column vectors of R...Ch. 4.2 - For each of the following linear operators on 2 ,...Ch. 4.2 - Determine the matrix representation of each of the...Ch. 4.2 - Let Y, P, and R be the yaw, pitch, and roll...Ch. 4.2 - Let L be the linear transformatino mapping P2 into...Ch. 4.2 - The linear transformation L defined by...Ch. 4.2 - Let S be the subspace of C[a,b] spanned by ex,xex...Ch. 4.2 - Let L be the linear operator on n . Suppose that...Ch. 4.2 - Let L be a linear operator on a vector space V....Ch. 4.2 - Let E=u1,u2,u3 and F=b1,b2 , where...Ch. 4.2 - Suppose that L1:VW and L2:WZ are linear...Ch. 4.2 - Let V and W be vector spaces with ordered bases E...Ch. 4.3 - For each of the following linear operators L on 2...Ch. 4.3 - Let u1,u2 and v1,v2 be ordered bases for 2 , where...Ch. 4.3 - Let L be the linear transformation on 3 defined by...Ch. 4.3 - Let L be the linear operator mapping 3 into 3...Ch. 4.3 - Let L be the operator on P3 defined by...Ch. 4.3 - Let V be the subspace of C[a,b] spanned by 1,ex,ex...Ch. 4.3 - Prove that if A is similar to B and B is similar...Ch. 4.3 - Suppose that A=SS1 , where is a diagonal matrix...Ch. 4.3 - Suppose that A=ST , where S is nonsingular. Let...Ch. 4.3 - Let A and B be nn matrices. Show that is A is...Ch. 4.3 - Show that if A and B are similar matrices, then...Ch. 4.3 - Let A and B t similar matrices. Show that (a) AT...Ch. 4.3 - Show that if A is similar to B and A is...Ch. 4.3 - Let A and B be similar matrices and let be any...Ch. 4.3 - The trace of an nn matrix A, denoted tr(A) , is...Ch. 4 - Use MATLAB to generate a matrix W and a vector x...Ch. 4 - Set A=triu(ones(5))*tril(ones(5)) . If L denotes...Ch. 4 - Prob. 3E Ch. 4 - For each statement that follows, answer true if...Ch. 4 - Prob. 2CTA Ch. 4 - Prob. 3CTA Ch. 4 - For each statement that follows, answer true if...Ch. 4 - Prob. 5CTA Ch. 4 - Prob. 6CTA Ch. 4 - Prob. 7CTA Ch. 4 - Prob. 8CTA Ch. 4 - Prob. 9CTA Ch. 4 - Prob. 10CTA Ch. 4 - Determine whether the following are linear...Ch. 4 - Prob. 2CTB Ch. 4 - Prob. 3CTB Ch. 4 - Prob. 4CTB Ch. 4 - Prob. 5CTB Ch. 4 - Prob. 6CTB Ch. 4 - Let L be the translation operator on 2 defined by...Ch. 4 - Let u1=[ 3 1 ],u2=[ 5 2 ] and let L be the linear...Ch. 4 - Let and and let L be the linear operator onwhose...Ch. 4 - Prob. 10CTB

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Let L be the translation operator on ℝ 2 defined by L ( x ) = x + a , where a = [ 2 5 ] Find the matrix representation of L with respect to the homogeneous coordinate system .

Solution Summary: The author explains the matrix representation of L with respect to the homogeneous coordinate system.

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