Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN: 9781305658004
Author: Ron Larson
Publisher: Cengage Learning
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Chapter 5.CM, Problem 1CM
To determine

(a)

To find:

The value of v+w and sketch the vector.

Expert Solution
Check Mark

Answer to Problem 1CM

Solution:

The value of v+w is (3,−7) and the graph of the vector is shown in figure (1).

Explanation of Solution

Given:

The vectors are as follows.

v=(1,−2)w=(2,−5)

Approach:

Add individual elements of the two vectors.

Calculation:

Find the value of v+w.

v+w=(1,−2)+(2,−5)=(1+2,−2−5)=(3,−7)

The following figure shows the graph of each vector.

Elementary Linear Algebra (MindTap Course List), Chapter 5.CM, Problem 1CM , additional homework tip 1

Figure (1)

Conclusion:

Hence, the value of v+w is (3,−7) and the graph of the vector is shown in figure (1).

To determine

(b)

To find:

The value of 3v.

Expert Solution
Check Mark

Answer to Problem 1CM

Solution:

The value of 3v is (3,−6) and the graph of the vector is shown in figure (2).

Explanation of Solution

Calculation:

Find 3v.

3v=3(1,−2)=(3,−6)

The following figure shows the graph of each vector.

Elementary Linear Algebra (MindTap Course List), Chapter 5.CM, Problem 1CM , additional homework tip 2

Figure (2)

Conclusion:

Hence, the value of 3v is (3,−6) and the graph of the vector is shown in figure (2).

To determine

(c)

To find:

The value of 2v−4w.

Expert Solution
Check Mark

Answer to Problem 1CM

Solution:

The value of 2v−4w is (−6,16) and graph of the vector is shown in figure (3).

Explanation of Solution

Calculation:

Find 2v−4w.

2v−4w=2(1,−2)−4(2,−5)=(2,−4)−(8,−20)=(2−8,−4+20)=(−6,16)

Therefore, the value of 2v−4w is (−6,16).

The following figure shows the graph of each vector.

Elementary Linear Algebra (MindTap Course List), Chapter 5.CM, Problem 1CM , additional homework tip 3

Figure (3)

Conclusion:

Hence, the value of 2v−4w is (−6,16) and graph of the vector is shown in figure (3).

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Chapter 5 Solutions

Elementary Linear Algebra (MindTap Course List)

Ch. 5.1 - Finding the Length of a Vector. In Exercises 1-4,...Ch. 5.1 - Finding the Length of a Vector. In Exercises 1-4,...Ch. 5.1 - Finding the Length of a Vector. In Exercises 1-4,...Ch. 5.1 - Finding the Length of a Vector. In Exercises 1-4,...Ch. 5.1 - Finding the Length of a Vector. In Exercises 5-8,...Ch. 5.1 - Finding the Length of a Vector. In Exercises 58,...Ch. 5.1 - Exercises Finding the Length of a Vector In...Ch. 5.1 - Exercises Finding the Length of a Vector In...Ch. 5.1 - Exercises Finding a Unit Vector. In Exercises 912,...Ch. 5.1 - Exercises Finding a Unit Vector. In Exercises 912,...
Ch. 5.1 - Exercises Finding a Unit Vector. In Exercises 912,...Ch. 5.1 - Exercises Finding a Unit Vector. In Exercises 912,...Ch. 5.1 - Exercises Finding a Vector. In Exercises 1316,...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Finding a VectorIn Exercises 13-16, find the...Ch. 5.1 - Consider the vector v=(1,3,0,4). Find u such that...Ch. 5.1 - For what values of c is c(1,2,3)=1?Ch. 5.1 - Finding the Distance Between Two VectorsIn...Ch. 5.1 - Finding the Distance Between Two VectorsIn...Ch. 5.1 - Finding the Distance Between Two VectorsIn...Ch. 5.1 - Finding the Distance Between Two VectorsIn...Ch. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Find (u+v)(2uv) when uu=4, uv=5, and vv=10.Ch. 5.1 - Find (3uv)(u3v) when uu=8, uv=7, and vv=6.Ch. 5.1 - Finding Lengths, Unit Vectors, and Dot Products In...Ch. 5.1 - Finding Lengths, Unit Vectors, and Dot Products In...Ch. 5.1 - Finding Lengths, Unit Vectors, and Dot Products In...Ch. 5.1 - Prob. 32ECh. 5.1 - Finding Lengths, Unit Vectors, and Dot Products In...Ch. 5.1 - Prob. 34ECh. 5.1 - Verifying the Cauchy-Schwarz Inequality In...Ch. 5.1 - Verifying the Cauchy-Schwarz Inequality In...Ch. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Finding the Angle Between Two Vectors In Exercises...Ch. 5.1 - Finding the Angle Between Two Vectors In Exercises...Ch. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Finding the Angle Between Two Vectors In Exercises...Ch. 5.1 - Finding the Angle Between Two Vectors In Exercises...Ch. 5.1 - Finding the Angle Between Two Vectors In Exercises...Ch. 5.1 - Prob. 46ECh. 5.1 - Determining a Relationship Between Two Vectors In...Ch. 5.1 - Determining a Relationship Between Two Vectors In...Ch. 5.1 - Prob. 49ECh. 5.1 - Determining a Relationship Between Two Vectors In...Ch. 5.1 - Prob. 51ECh. 5.1 - Determining a Relationship Between Two Vectors In...Ch. 5.1 - Exercises Determining a relationship Between Two...Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Exercises Finding orthogonal Vectors In Exercises...Ch. 5.1 - Exercises Finding orthogonal Vectors In Exercises...Ch. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Verifying the Triangle Inequality. In Exercises...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - Verifying the Pythagorean Theorem In Exercises...Ch. 5.1 - Prob. 65ECh. 5.1 - Prob. 66ECh. 5.1 - Rework Exercise 23 using matrix multiplication....Ch. 5.1 - Rework Exercise 24 using matrix multiplication....Ch. 5.1 - Prob. 69ECh. 5.1 - Prob. 70ECh. 5.1 - Writing In Exercises 71 and 72, determine whether...Ch. 5.1 - Prob. 72ECh. 5.1 - True or False?In Exercises 73 and 74, determine...Ch. 5.1 - Prob. 74ECh. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Orthogonal Vectors In Exercises 77 and 78, let...Ch. 5.1 - Orthogonal Vectors In Exercises 77 and 78, let...Ch. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.1 - Prob. 82ECh. 5.1 - Guided Proof Prove that if u is orthogonal to v...Ch. 5.1 - Prob. 84ECh. 5.1 - Prob. 85ECh. 5.1 - Proof Prove that u+v=u+v if and only if u and v...Ch. 5.1 - Proof Use the properties of matrix multiplication...Ch. 5.1 - Prob. 88ECh. 5.1 - Writing Let x be a solution to mn homogeneous...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Showing That a Function Is an Inner ProductIn...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Showing That a Function Is Not an Inner Product In...Ch. 5.2 - Prob. 16ECh. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Prob. 18ECh. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Prob. 22ECh. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Prob. 26ECh. 5.2 - Showing That a Function Is an Inner ProductIn...Ch. 5.2 - Showing That a Function Is an Inner ProductIn...Ch. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Prob. 30ECh. 5.2 - Finding Inner Product, Length, and DistanceIn...Ch. 5.2 - Finding Inner Product, Length, and Distance In...Ch. 5.2 - Showing That a Function Is an Inner Product In...Ch. 5.2 - Prob. 34ECh. 5.2 - Finding Inner Product, Length, and Distance In...Ch. 5.2 - Finding Inner Product, Length, and Distance In...Ch. 5.2 - Finding Inner Product, Length, and Distance In...Ch. 5.2 - Prob. 38ECh. 5.2 - Calculus In Exercises 39-42, use the functions f...Ch. 5.2 - 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Prob. 66ECh. 5.2 - Calculus In Exercises 65-68, show that f and g are...Ch. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Finding and Graphing Orthogonal Projections in R2...Ch. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Finding Orthogonal Projections In Exercises 7376,...Ch. 5.2 - Finding Orthogonal Projections In Exercises 7376,...Ch. 5.2 - Prob. 76ECh. 5.2 - Prob. 77ECh. 5.2 - Calculus In Exercises 77-84, find the orthogonal...Ch. 5.2 - Calculus In Exercises 77-84, find the orthogonal...Ch. 5.2 - Prob. 80ECh. 5.2 - Prob. 81ECh. 5.2 - Prob. 82ECh. 5.2 - Prob. 83ECh. 5.2 - Prob. 84ECh. 5.2 - True or false?In Exercises 85 and 86, determine...Ch. 5.2 - Prob. 86ECh. 5.2 - Prob. 87ECh. 5.2 - Prob. 88ECh. 5.2 - Prob. 89ECh. 5.2 - Proof Let u and v be a nonzero vectors in an inner...Ch. 5.2 - Prob. 91ECh. 5.2 - Prob. 92ECh. 5.2 - Prob. 93ECh. 5.2 - Prob. 94ECh. 5.2 - Guided proofLet u,v be the Euclidean inner product...Ch. 5.2 - CAPSTONE (a) Explain how to determine whether a...Ch. 5.2 - 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Prob. 20ECh. 5.3 - Finding a Coordinate Matrix In Exercises 19-24,...Ch. 5.3 - Finding a Coordinate Matrix In Exercises 19-24,...Ch. 5.3 - Prob. 23ECh. 5.3 - Finding a Coordinate Matrix In Exercises 19-24,...Ch. 5.3 - Applying the Gram-Schmidt Process In Exercises...Ch. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Applying the Gram-Schmidt Process In Exercises...Ch. 5.3 - Prob. 40ECh. 5.3 - Use the inner product u,v=2u1v1+u2v2 in R2 and...Ch. 5.3 - WritingExplain why the result of Exercise 41 is...Ch. 5.3 - Calculus In Exercises 43-48, let B={1,x,x2} be a...Ch. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Calculus In Exercises 43-48, let B={1,x,x2} be a...Ch. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Applying the Alternative Form of the Gram-Schmidt...Ch. 5.3 - Prob. 52ECh. 5.3 - Applying the Alternative Form of the Gram-Schmidt...Ch. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - True or False? 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In Exercises 43and 44, determine...Ch. 5.4 - True or false? In Exercises 43 and 44, determine...Ch. 5.4 - Proof Prove that if S1 and S2 are orthogonal...Ch. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.5 - Finding the Cross Product In Exercises 1-6, find...Ch. 5.5 - Prob. 2ECh. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Prob. 24ECh. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - 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Prob. 90ECh. 5.5 - Prob. 91ECh. 5.5 - Prob. 92ECh. 5.5 - Use your schools library, the Internet, or some...Ch. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Finding Lengths, Dot Product, and Distance In...Ch. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Prob. 18CRCh. 5.CR - Finding the Angle Between Two VectorsIn Exercises...Ch. 5.CR - Finding the Angle Between Two Vectors In Exercises...Ch. 5.CR - Prob. 21CRCh. 5.CR - Prob. 22CRCh. 5.CR - Prob. 23CRCh. 5.CR - Prob. 24CRCh. 5.CR - For u=(4,32,1) and v=(12,3,1), a find the inner...Ch. 5.CR - For u=(0,3,13) and v=(43,1,3), a find the inner...Ch. 5.CR - 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Prob. 50CRCh. 5.CR - Prob. 51CRCh. 5.CR - Prob. 52CRCh. 5.CR - Prob. 53CRCh. 5.CR - Let V be an two dimensional subspace of R4 spanned...Ch. 5.CR - Prob. 55CRCh. 5.CR - Prob. 56CRCh. 5.CR - Prob. 57CRCh. 5.CR - Prob. 58CRCh. 5.CR - Prob. 59CRCh. 5.CR - Find the projection of the vector v=[102]T onto...Ch. 5.CR - Find the bases for the four fundamental subspaces...Ch. 5.CR - Prob. 62CRCh. 5.CR - Prob. 63CRCh. 5.CR - Prob. 64CRCh. 5.CR - Finding the Cross Product In Exercises 65-68, find...Ch. 5.CR - Finding the Cross Product In Exercises 65-68, find...Ch. 5.CR - Prob. 67CRCh. 5.CR - Finding the Cross Product In Exercises 65-68, find...Ch. 5.CR - Prob. 69CRCh. 5.CR - Prob. 70CRCh. 5.CR - Finding the Volume of a ParallelepipedIn Exercises...Ch. 5.CR - Prob. 72CRCh. 5.CR - Prob. 73CRCh. 5.CR - Prob. 74CRCh. 5.CR - Finding a Least Approximation In Exercises 75-78,...Ch. 5.CR - Finding a Least Approximation In Exercises 75-78,...Ch. 5.CR - Prob. 77CRCh. 5.CR - Finding a Least Approximation In Exercises 75-78,...Ch. 5.CR - Finding a Least Squares Approximation In Exercises...Ch. 5.CR - Finding a Least Squares Approximation In Exercises...Ch. 5.CR - Prob. 81CRCh. 5.CR - Prob. 82CRCh. 5.CR - Prob. 83CRCh. 5.CR - Prob. 84CRCh. 5.CM - Prob. 1CMCh. 5.CM - Take this test to review the material in Chapters...Ch. 5.CM - Take this test to review the material in Chapters...Ch. 5.CM - Use a software program or a graphing utility to...Ch. 5.CM - Take this test to review the material in Chapters...Ch. 5.CM - Prob. 6CMCh. 5.CM - Prob. 7CMCh. 5.CM - Take this test to review the material in Chapters...Ch. 5.CM - Take this test to review the material in Chapters...Ch. 5.CM - Prob. 10CMCh. 5.CM - Prob. 11CMCh. 5.CM - Prob. 12CMCh. 5.CM - Prob. 13CMCh. 5.CM - Prob. 14CMCh. 5.CM - Prob. 15CMCh. 5.CM - Prob. 16CMCh. 5.CM - Prob. 17CMCh. 5.CM - Prob. 18CMCh. 5.CM - Prob. 19CMCh. 5.CM - Prob. 20CMCh. 5.CM - Prob. 21CMCh. 5.CM - The two matrices A and B are row-equivalent....Ch. 5.CM - Prob. 23CMCh. 5.CM - Prob. 24CM
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