Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
5th Edition
ISBN: 9780134689531
Author: Lee Johnson, Dean Riess, Jimmy Arnold
Publisher: PEARSON
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Chapter 2.2, Problem 1E
In Exercises 1-4, plot the points
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You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Chapter 2 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 2.1 - In Exercises 1-4, graph the geometric vector u=AB...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Let u=AB and v=CD where...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - In Exercises 1114, express the geometric vector...Ch. 2.1 - In Exercises 1114, express the geometric vector...Ch. 2.1 - Prob. 14ECh. 2.1 - In Exercises 15-16, find B=(b1,b2) such that v=AB....Ch. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Let u=[13] and v=[22], and let A denote the point...Ch. 2.1 - Prob. 20ECh. 2.1 - Let u=ABandv=CD, where...Ch. 2.1 - Prob. 22ECh. 2.1 - Let u=[13] and v=[22], and let A denote the point...Ch. 2.1 - Let u=AB and v=CD, where A=(1,2), B=(3,5),...Ch. 2.1 - Let v=[32], and let A=(0,5). aFind points B and C...Ch. 2.1 - Let v=2i+6j and let A=(2,1). aFind points B and C...Ch. 2.1 - Prob. 27ECh. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - Prob. 31ECh. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 36-39, find the components of u+v and...Ch. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Let u=[ab] where at least one of a or b is...Ch. 2.2 - In Exercises 1-4, plot the points P and Q and...Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - In Exercise 5-6, find the coordinates of the...Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 13-16, graph the given region R....Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - In the Exercises 18-21, a give the algebraic...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - Prob. 4ECh. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - Prob. 11ECh. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - Prob. 18ECh. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - In Exercises 23-26, find u1 and u2 such that...Ch. 2.3 - In Exercises 23-26, find u1 and u2 such that...Ch. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - In the Exercises 32-35, calculate the cross...Ch. 2.3 - Prob. 35ECh. 2.3 - In the Exercises 36-39, find the vector w such...Ch. 2.3 - In the Exercises 36-39, find the vector w such...Ch. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - In Exercises 40-41, find a vector w that is...Ch. 2.3 - In Exercises 40-41, find a vector w that is...Ch. 2.3 - In Exercises 42-43, two sides of a parallelogram...Ch. 2.3 - In Exercises 42-43, two sides of a parallelogram...Ch. 2.3 - In Exercises 44-45, find the area of the triangle...Ch. 2.3 - In Exercises 44-45, find the area of the triangle...Ch. 2.3 - In Exercises 46-47, three edges of a...Ch. 2.3 - In Exercises 46-47, three edges of a...Ch. 2.3 - In Exercises 48-49, determine if the three vectors...Ch. 2.3 - In Exercises 48-49, determine if the three vectors...Ch. 2.3 - Verify that x=u2v3u3v2,y=u3v1u1v3,z=u1v2u2v1, is...Ch. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.4 - In Exercises 1-2, give parametric equations for...Ch. 2.4 - In Exercises 1-2, give parametric equations for...Ch. 2.4 - In Exercises 3-4, give parametric equations for...Ch. 2.4 - In Exercises 3-4, give parametric equations for...Ch. 2.4 - Prob. 5ECh. 2.4 - In Exercises 5-8, determine whether the given...Ch. 2.4 - Prob. 7ECh. 2.4 - In Exercises 5-8 determine whether the given lines...Ch. 2.4 - In Exercises 9-10, find parametric equations for...Ch. 2.4 - In Exercises 910, find parametric equations for...Ch. 2.4 - In Exercises 1114, find a point P where the line...Ch. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - In Exercises 1516, find the equation of the plane...Ch. 2.4 - Prob. 17ECh. 2.4 - P=(5,1,7) Q=(6,9,2) R=(7,2,9) In Exercises 1720,...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - In Exercises 21-22, find a unit normal for the...Ch. 2.4 - Prob. 23ECh. 2.4 - In Exercises 23-24, find the equation of the plane...Ch. 2.4 - Prob. 25ECh. 2.4 - In Exercises 25-26, the given planes intersect in...Ch. 2.SE - Let u=[52],v=[71],x=[14] Write x in terms of...Ch. 2.SE - Prob. 2SECh. 2.SE - Let P=(16,20) and Q=(12,8), find Coordinates of...Ch. 2.SE - Prob. 4SECh. 2.SE - Prob. 5SECh. 2.SE - Prob. 6SECh. 2.SE - Prob. 7SECh. 2.SE - Prob. 8SECh. 2.SE - Prob. 9SECh. 2.SE - Prob. 10SECh. 2.SE - Prob. 11SECh. 2.SE - Prob. 12SECh. 2.SE - LetA, B, C,andDbe vertices, not endpoints of a...Ch. 2.CE - True or False : if uv=0, then either u=0orv=0.Ch. 2.CE - Prob. 2CECh. 2.CE - Prove the Parallelogram Law :...Ch. 2.CE - Let u and v be nonzero vectors in the plane....Ch. 2.CE - Prob. 5CECh. 2.CE - Prob. 6CECh. 2.CE - Prob. 7CECh. 2.CE - Prob. 8CECh. 2.CE - Prob. 9CECh. 2.CE - Prob. 10CECh. 2.CE - Prob. 11CECh. 2.CE - Prob. 12CE
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