Linear Algebra With Applications (class...5th EditionBRETSCHER, OTTO Publisher: Pearson Education, Inc.,ISBN: 9780135162972
Linear Algebra With Applications (class...
Solutions for Linear Algebra With Applications (classic Version)
Problem 1E:
Sketch the image of the standard L under the lineartransformation T(x)=[3112]x . See Example 1.Problem 3E:
Consider a linear transformation T from 2 to 3 . Use T(e1) and T(e2) to describe the image of the...Problem 5E:
The matrix [0.80.60.60.8] represents a rotation. Find the angle of rotation (inradians).Problem 6E:
Let L be the line in 3 that consists of all scalar multiplies of the vector [212] . Find the...Problem 7E:
Let L be the line in 3 that consists of all scalar multipliesof [212] . Find the reflection of the...Problem 10E:
Find the matrix of the orthogonal projection onto theline L in 2 shown in the accompanying figure:Problem 12E:
Consider a reflection matrix A and a vector x in 2 . Wedefine v=x+Ax and w=xAx . a. Using the...Problem 13E:
Suppose a line L in 2 contains the Unit vector u=[u1u2] . Find the matrix A of the linear...Problem 14E:
Suppose a line L in 3 contains the unit vector u=[u1u2u3] . a. Find the matrix A of the linear...Problem 15E:
Suppose a line L in 3 contains the unit vector u=[u1u2u3] . Find the matrix A of the linear...Problem 16E:
Let T(x)=refL(x) be the reflection about the line L in 2 shown in the accompanying figure. a. Draw...Problem 17E:
Consider a matrix A of the form A=[abba] , where a2+b2=1 . Find two nonzero perpendicular vectors v...Problem 18E:
The linear transformation T(x)=[0.60.80.80.6]x is a reflection about a line L. See Exercise 17. Find...Problem 19E:
Find the matrices of the linear transformations from 3to3given in Exercises 19 through 23. Some of...Problem 20E:
Find the matrices of the linear transformations from 3to 3given in Exercises 19 through 23. Some of...Problem 21E:
Find the matrices of the linear transformations from 3to 3given in Exercises 19 through 23. Some of...Problem 22E:
Find the matrices of the linear transformations from 3to 3given in Exercises 19 through 23. Some of...Problem 23E:
Find the matrices of the linear transformations from 3to 3given in Exercises 19 through 23. Some of...Problem 24E:
Rotations and reflections have two remarkable properties: They preserve the length of vectors and...Problem 25E:
Find the inverse of the matrix [1k01] ,where k is anarbitrary constant. Interpret your result...Problem 26E:
a. Find the scaling matrix A that transforms [21] into [84] . b. Find the orthogonal projection...Problem 32E:
Consider the rotation matrix D=[cossinsincos] and the vector v=[cossin] , where and are arbitrary...Problem 33E:
Consider two nonparallel lines L1 and L2 in 2 .Explain why a vector v in 2 can be expresseduniquely...Problem 34E:
One of the five given matrices represents an orthogonalprojection onto a line and another represents...Problem 38E:
The determinant of a matrix [abcd] is adbc (wehave seen this quantity in Exercise 2.1.13 already)....Problem 39E:
Describe each of the linear transformations defined by the matrices in parts (a) through (e)...Problem 44E:
A nonzero matrix of the form A=[abba] represents a rotation combined with a scaling. Use the formula...Browse All Chapters of This Textbook
Chapter 1 - Linear EquationsChapter 1.1 - Introduction To Linear SystemsChapter 1.2 - Matrices, Vectors, And Gauss–jordan EliminationChapter 1.3 - On The Solutions Of Linear Systems; Matrix AlgebraChapter 2 - Linear TransformationsChapter 2.1 - Introduction To Linear Transformations And Their InversesChapter 2.2 - Linear Transformations In GeometryChapter 2.3 - Matrix ProductsChapter 2.4 - The Inverse Of A Linear TransformationChapter 3 - Subspaces Of Rn And Their Dimensions
Chapter 3.1 - Image And Kernel Of A Linear TransformationChapter 3.2 - Subspaces Of Rn; Bases And Linear IndependenceChapter 3.3 - The Dimension Of A Subspace Of RnChapter 3.4 - CoordinatesChapter 4 - Linear SpacesChapter 4.1 - Introduction To Linear SpacesChapter 4.2 - Linear Transformations And IsomorphismsChapter 4.3 - The Matrix Of A Linear TransformationChapter 5 - Orthogonality And Least SquaresChapter 5.1 - Orthogonal Projections And Orthonormal BasesChapter 5.2 - Gram–schmidt Process And Qr FactorizationChapter 5.3 - Orthogonal Transformations And Orthogonal MatricesChapter 5.4 - Least Squares And Data FittingChapter 5.5 - Inner Product SpacesChapter 6 - DeterminantsChapter 6.1 - Introduction To DeterminantsChapter 6.2 - Properties Of The DeterminantChapter 6.3 - Geometrical Interpretations Of The Determinant; Cramer’s RuleChapter 7 - Eigenvalues And EigenvectorsChapter 7.1 - DiagonalizationChapter 7.2 - Finding The Eigenvalues Of A MatrixChapter 7.3 - Finding The Eigenvectors Of A MatrixChapter 7.4 - More On Dynamical SystemsChapter 7.5 - Complex EigenvaluesChapter 7.6 - StabilityChapter 8 - Symmetric Matrices And Quadratic FormsChapter 8.1 - Symmetric MatricesChapter 8.2 - Quadratic FormsChapter 8.3 - Singular ValuesChapter 9.1 - An Introduction To Continuous Dynamical SystemsChapter 9.2 - The Complex Case: Euler’s FormulaChapter 9.3 - Linear Differential Operators And Linear Differential Equations
Sample Solutions for this Textbook
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More Editions of This Book
Corresponding editions of this textbook are also available below:
Linear Algebra With Applications (edn 3)
3rd Edition
ISBN: 9788131714416
Student's Solutions Manual for Linear Algebra with Applications
3rd Edition
ISBN: 9780131453364
Linear Algebra With Applications, Student Solutions Manual
2nd Edition
ISBN: 9780130328564
Linear Algebra With Applications, 4th Edition
4th Edition
ISBN: 9780136009269
Linear Algebra And Application
98th Edition
ISBN: 9780135762738
Linear algebra
97th Edition
ISBN: 9780131907294
Linear Algebra With Applications
5th Edition
ISBN: 9781292022147
Linear Algebra With Applications
5th Edition
ISBN: 9780321796967
EBK LINEAR ALGEBRA WITH APPLICATIONS (2
5th Edition
ISBN: 8220100578007
EBK LINEAR ALGEBRA WITH APPLICATIONS (2
5th Edition
ISBN: 9780321916914
Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
EBK LINEAR ALGEBRA WITH APPLICATIONS (2
5th Edition
ISBN: 9780100578005
Linear Algebra With Applications
5th Edition
ISBN: 9780321796943
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