Wondershare PDFelementFile Home HelpT Add TextElementary_..._lib_org.pdf x +BookmarkAdd□ OΣΣΣΣΣΣA+ ACoverApplications and HistoricalTopicsTitle PageCopyrightAbout the AuthorsPrefaceContents> 1: Systems of Linear Equationsand Matrices>2: Determinants>3: Euclidean Vector Spaces>4: General Vector Spaces> 5: Eigenvalues andEigenvectors>6: Inner Product Spaces7: Diagonalization andQuadratic FormsAdd Image Link>> 8: General LinearTransformations>9: Numerical MethodsAppendix A: Working withProofsseElementary_Linear_Algebra_by_Howard_Anton, Anton_Kaul_z_lib_org.pdfComment Edit Convert Tool View Form Protect Page TemplateWatermarkBackgroundInHeader & Footer 1 Bates NumberAt least one signature has problems.23. The accompanying figure shows a rectangular xy-coordin-ate system determined by the unit basis vectors i and j andan x'y'-coordinate system determined by unit basis vectorsu₁ and u₂. Find the x'y'-coordinates of the points whosexy-coordinates are given.a. (√3,1)b. (1,0)c. (0,1) d. (a,b)Ay and y'j and u₂30°xFIGURE Ex-2324. The accompanying figure shows a rectangular xy-coordinatesystem and an x'y'-coordinate system with skewed axes.Assuming that 1-unit scales are used on all the axes, find thex'y'-coordinates of the points whose xy-coordinates are given.a. (1,1) b. (1,0) c. (0,1) d. (a, b)APOu₁iPhone/iPadBuy NowEdit Mode4.5 Coordinates and Basis 247a. Find w if S is the basis in Exercise 2.b. Find q if S is the basis in Exercise 3.c. Find B if S is the basis in Exercise 5.28. The basis that we gave for M₂2 in Example 4 consisted of non-invertible matrices. Do you think that there is a basis for M22consisting of invertible matrices? Justify your answer.Working with Proofs29. Prove that R* is an infinite-dimensional vector space.30. Let TARR" be multiplication by an invertible matrixA, and let {u₁, ₂,..., u} be a basis for R". Prove that{TA(U₁), TA (U₂),..., TA (un)} is also a basis for R".31. Prove that if V is a subspace of a vector space W and if V isinfinite-dimensional, then so is W.True-False ExercisesTF. In parts (a)-(e) determine whether the statement is true orfalse, and justify your answer.a. If V = span{v₁,...,Vn}, then {v₁,...,v} is a basis for V.b. Every linearly independent subset of a vector space V is abasis for V.Search ToolsEditJump to SignatureReadLog Inx

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23. The accompanying figure shows a rectangular xy-coordin- ate system determined by the unit basis vectors i and j and an x'y-coordinate system determined by unit basis vectors u, and u₂. Find the x'y'-coordinates of the points whose xy-coordinates are given. a. (√3,1) b. (1,0) c. (0,1) d. (a,b) Ay and y' X jand u₂ 30° u₁

23. The accompanying figure shows a rectangular xy-coordin- ate system determined by the unit basis vectors i and j and an x'y-coordinate system determined by unit basis vectors u, and u₂. Find the x'y'-coordinates of the points whose xy-coordinates are given. a. (√3,1) b. (1,0) c. (0,1) d. (a,b) Ay and y' X jand u₂ 30° u₁

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Wondershare PDFelement
File Home Help
T Add Text
Elementary_..._lib_org.pdf x +
Bookmark
Add
□ O
ΣΣΣΣΣΣ
A+ A
Cover
Applications and Historical
Topics
Title Page
Copyright
About the Authors
Preface
Contents
> 1: Systems of Linear Equations
and Matrices
>
2: Determinants
>
3: Euclidean Vector Spaces
>4: General Vector Spaces
> 5: Eigenvalues and
Eigenvectors
>
6: Inner Product Spaces
7: Diagonalization and
Quadratic Forms
Add Image Link
>
> 8: General Linear
Transformations
>9: Numerical Methods
Appendix A: Working with
Proofs
se
Elementary_Linear_Algebra_by_Howard_Anton, Anton_Kaul_z_lib_org.pdf
Comment Edit Convert Tool View Form Protect Page Template
Watermark
Background
In
Header & Footer 1 Bates Number
At least one signature has problems.
23. The accompanying figure shows a rectangular xy-coordin-
ate system determined by the unit basis vectors i and j and
an x'y'-coordinate system determined by unit basis vectors
u₁ and u₂. Find the x'y'-coordinates of the points whose
xy-coordinates are given.
a. (√3,1)
b. (1,0)
c. (0,1) d. (a,b)
Ay and y'
j and u₂
30°
x
FIGURE Ex-23
24. The accompanying figure shows a rectangular xy-coordinate
system and an x'y'-coordinate system with skewed axes.
Assuming that 1-unit scales are used on all the axes, find the
x'y'-coordinates of the points whose xy-coordinates are given.
a. (1,1) b. (1,0) c. (0,1) d. (a, b)
APO
u₁
iPhone/iPad
Buy Now
Edit Mode
4.5 Coordinates and Basis 247
a. Find w if S is the basis in Exercise 2.
b. Find q if S is the basis in Exercise 3.
c. Find B if S is the basis in Exercise 5.
28. The basis that we gave for M₂2 in Example 4 consisted of non-
invertible matrices. Do you think that there is a basis for M22
consisting of invertible matrices? Justify your answer.
Working with Proofs
29. Prove that R* is an infinite-dimensional vector space.
30. Let TARR" be multiplication by an invertible matrix
A, and let {u₁, ₂,..., u} be a basis for R". Prove that
{TA(U₁), TA (U₂),..., TA (un)} is also a basis for R".
31. Prove that if V is a subspace of a vector space W and if V is
infinite-dimensional, then so is W.
True-False Exercises
TF. In parts (a)-(e) determine whether the statement is true or
false, and justify your answer.
a. If V = span{v₁,...,Vn}, then {v₁,...,v} is a basis for V.
b. Every linearly independent subset of a vector space V is a
basis for V.
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Read
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