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Chapter 1 Neither answer explanation Echelon Form Reduced Echelon Form solve
Exam Name___________________________________ 1) A company manufactures two products. For $1.00 worth of product A, the company spends $0.40 on materials, $0.30 on labor, and $0.15 on overhead. For $1.00 worth of product B, the company spends $0.40 on materials, $0.25 […]
Chapter 2 Rotate Points Through 45 And Then Scale
Exam Name___________________________________ 1) A = 4 0 1 2 –1–3 5 3 7 , B =–2 0 8 5 1 6 2 2 4 –1 0 3 1) A) –4–1 32 23 –17 –3 14 –1 21 11 46 52 […]
Chapter 3 explanation determine The Values The
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute the determinant of the matrix by cofactor expansion. 1) 2–2 6 4 2 2 7 1 6–614 14 –2 2 –6 1 […]
Chapter 4 Determine which of the sets of vectors is linearly
Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 1) A mathematician has found 4 solutions to a homogeneous system of 36 equations in 39 variables. The 4 […]
Chapter 5 Saddle point; direction of greatest attraction
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue. 1) A =1– 4 – 4 – […]
Chapter 6 Exam Name Multiple Choice Choose The One
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a QR factorization of the matrix A. 1) A = 0 1 1 1 1 0 –1–1 1 1 –1 1 1) […]
Chapter 7 Find the singular values of the matrix
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a singular value decomposition of the matrix A. 1) A =–9 0 0 5 1) A) A = 1 0 0 1 […]
Chapter 8 Pick a set S of four distinct points in 3 such
Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it. 1) 1 1, 3 5, […]
Chapter 9 The slack variable x5 which corresponds to the
Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) A set S in Rn is convex if, for each p and q in S, the line […]
Education Calculator Homework Determine Diagonalizable Explain 1
INSTRUCTOR’S TI CALCULATOR MANUAL MICHAEL MILLER Corban University LUZ DEALBA Drake University LINEAR ALGEBRA AND ITS APPLICATIONS FOURTH EDITION David C. Lay University of Maryland The author and publisher of this book have used their best efforts in preparing this […]
Education Calculator Homework Nul Explain L Use Your Calculator Find
TI Project: Cryptography The problems in this project will help you to reinforce row operation techniques and to appreciate the value of the inverse of a matrix and determinants in applications, such as message coding. Review Sections 2.2, 3.1, 3.2 […]
Education Calculator Homework Run the program DWMT —it uses B as the input—to view
TI Project: Linear Transformations 1 TI Project: Linear Transformations The problems will help you to visualize the action of linear transformations on the plane, and to view matrices as functions acting on vectors. Review Sections 1.8 and 1.9 of the […]
Education Calculator Homework The problems will help you to reinforce the concepts of
5. References [1] D. Carlson, C. R. Johnson, D. C. Lay, A. D. Porter, Ann E. Watkins, and William Watkins, eds., “Resources for Teaching Linear Algebra“, MAA Notes #42, Mathematical Association of America, Washington, D.C., 1999. [2] D. Carlson, C. […]
Education Chapter 1 Homework For instance, if the first column concerns the population in the city
Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 7. Loop 1: The resistance vector is 22 1 3 4 4 7Voltage drop for is negative; flows in opposite direction 0Current does not flow in loop 1 Voltage drop for […]
Education Chapter 1 Homework See the parallelograms drawn on the figure from the text that accompanies this
1.3 • Solutions 21 3100 6400 23610 ~ 0 1.000 1.800 250 360 1623 0 0 0 ⎢⎥⎢⎥ ⎢⎥⎢⎥ ⎢⎥⎢⎥ ⎣⎦⎣⎦ The steam plant burned 3.9 tons of anthracite coal and 1.8 tons of bituminous coal. 27.6 30.2 162 1.000 […]
Education Chapter 1 Homework The entries in each column must sum to
1.6 • Solutions 41 Move all variables to the left side and combine like terms: –.8 .9 – .4 0 –.1 – .8 .6 0 FMS FMS pp p pp p += += .8 .9 .4 0 .1 .8 .6 […]
Education Chapter 1 Homework The fourth equation is x4 = –5, and the other
1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 19–22, and 25. For brevity, the symbols R1, R2,…, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at […]
Education Chapter 1 Homework This image point lies in the parallelogram determined by T(u) and T(v)
1.8 • Solutions 61 which is not the same as T(x) + T(y) = Ax + b + Ay + b 25. Any point x on the line through p in the direction of v satisfies the parametric equation x […]
Education Chapter 2 Homework False The And Also Need Switched 13
2.3 • Solutions 107 ( ) ( ( )) ( ( )) Because is linear Byequation (1) () Sr SrT STr T r rS == = = ux x x u So S preserves scalar multiples. Thus S is a […]
Education Chapter 2 Homework Also, you could ask students to explain why an n×n matrix with linearly
r 2.1 SOLUTIONS Notes: The definition here of a matri x calculations. (The dual fact about the r o vectors here are usually written as c o reinforce the definition of AB. o ws of A and the rows of […]
Education Chapter 2 Homework Since Q is square and QTQ = I, Q is invertible by the Invertible Matrix Theorem
2.5 • Solutions 127 1 100 100 ~0 1 0 2 1 0 , 001 111 IL − ⎡⎤ ⎢⎥ ⎡⎤ =⎣⎦ ⎢⎥ ⎢⎥ − ⎣⎦ 1 100 so 2 1 0 . 111 L − ⎡ ⎤ ⎢ ⎥ […]
Education Chapter 2 Homework This shows that the columns of V are linearly independent
2.8 • Solutions 147 5. The vector w is in the subspace generated by v 1 and v 2 if and only if the vector equation x 1 v 1 + x 2 v 2 = w is consistent. The […]
Education Chapter 3 Homework Since this is a triangular matrix, we have found that 1det
182 CHAPTER 3 • Determinants 5. The system is equivalent to Ax = b, where 210 301 012 A ⎡ ⎤ ⎢ ⎥ =− ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ and 7 8 3 ⎡ ⎤ ⎢ ⎥ =− ⎢ […]
Education Chapter 3 Homework There are many ways to do this determinant efficiently
3.1 SOLUTIONS Notes: Some exercises in this section provide practice in computing determinants, while others allow the student to discover the properties of determinants which will be studied in the next section. Determinants are developed through the cofactor expansion, which […]
Education Chapter 4 Homework Note that u and v are on the line L, but u + v is not
r 4.1 SOLUTIONS Notes: This section is designed to avoi axioms on an array of sets. Theorem 1 p set is a subspace. Students should be ta u (and the next few sections) emphasize vectors do appear later in the […]
Education Chapter 4 Homework By inspection we note that this set is linearly independent
4.3 • Solutions 217 2 32 4 4 5 10 , 02 01 00 x xx x x x ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ == + ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ […]
Education Chapter 4 Homework If S is a finite spanning set for V, then a subset of S
4.8 • Solutions 255 6876 .35 .5 .35 .35(3) .5(.7) .35(0) 1.4,zyyy=++= ++ = 7987 .35 .5 .35 .35(.7) .5(3) .35(.7) 2,zyyy=++= ++ = 81098 .35 .5 .35 .35(0) .5(.7) .35(3) 1.4,zyyy=++=++=… b. This signal is two times the signal […]
Education Chapter 4 Homework This is an important section for engineering students and worth extra class
4.6 • Solutions 237 A basis for Row A is the pivot rows of B: { } (2,6, 6,6,3,6),(0,3,0,3,3,0),(0,0,0,0,3,0) .− To find a basis for Nul A row reduce to reduced echelon form: 01 0100 . 00 0010 00 0000 […]
Education Chapter 5 Homework An estimate for the corresponding eigenvector is
5.8 • Solutions 345 Solving this equation for Ax, we find that 11 () ⎛⎞ ⎛ ⎞ =+=+ ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ xxx xA αµ α µµ Thus (1 ) α µ λ= + / is an eigenvalue […]
Education Chapter 5 Homework If the eigenvalues close to 4 and 4− have different absolute
5.7 • Solutions 333 (3 ) ( 3 ) 12 33 33 22 it it ii cec e − −+ −− ⎡⎤ ⎡⎤ + ⎢⎥ ⎢⎥ ⎣⎦ ⎣⎦ where 1 c and 2 c are arbitrary complex numbers. To build […]
Education Chapter 5 Homework Since A is triangular, its eigenvalues are 2
5.3 • Solutions 293 14. The eigenvalues of A are given to be 2 and 3. For λ = 2: 00 2 2112, 00 1 AI − ⎡⎤ ⎢⎥ −= ⎢⎥ ⎢⎥ ⎣⎦ ⎣ ⎦ general solution is 2 1 […]
Education Chapter 5 Homework The entries in a solution satisfy
r 5.1 SOLUTIONS Notes : Exercises 1–6 reinforce the d e eigenvectors and difference equations, a example and anticipates discussions of d 1. The number 2 is an eigenvalue of A This equation is equivalent to (−A 32 20 238 […]
Education Chapter 5 Homework The Study Guide points out that the matrix C is described in Theorem 9
5.5 • Solutions 313 3. 51 . 81 A⎡⎤ =⎢⎥ − ⎣⎦ The characteristic polynomial is 2 613,−+ so the eigenvalues of A are 63652 32. 2i ±− ==± For λ = 3 + 2i: 22 1 (3 2 ) […]
Education Chapter 6 Homework Next, suppose Ax = b is consistent
r 6.1 SOLUTIONS Notes: The first half of this section is c concepts of orthogonality and orthogon a an important general fact, but is needed in Section 7.4. The optional material on 1. Since 1 2 − ⎡⎤ =⎢⎥ ⎣⎦ […]
Education Chapter 6 Homework The orthogonal projection ˆp2 of 2p onto the subspace
6.7 • Solutions 391 6.7 SOLUTIONS Notes : The three types of inner products described here (in Examples 1, 2, and 7) are matched by examples in Section 6.8. It is possible to spend just one day on selected portions […]
Education Chapter 6 Homework This process will continue until m – n vectors have
6.4 • Solutions 377 1/ 5 0 0 5545 ,062 1/ 5 1/2 1/2 004 1/ 5 1/2 1/2 1/ 5 1/2 1/2 T QRQA ⎡ ⎤ − ⎢⎥ − ⎢ ⎥ ⎢⎥ ===− − ⎢ ⎥ ⎢⎥ ⎢ ⎥ […]
Education Chapter 7 Homework Then P orthogonally diagonalizes A, and
r 7.1 SOLUTIONS Notes: Students can profit by reviewin working on this section. Theorems 1 an d sections that follow. Note that symmetri c text have real entries, as mentioned at been constructed so that mastery of the G Theorem […]
Education Chapter 7 Homework First note that the determinant of an orthogonal matrix is ±1
7.4 • Solutions 439 1/ 2 1/ 2 25: , 9: 1/ 2 1/ 2 ⎡⎤ ⎡ ⎤ − == ⎢⎥ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎣⎦ ⎣ ⎦ Thus one choice for V is 1/ 2 1/ 2 . […]
Education Chapter 7 Homework Theorem 8 is needed at the very end of Section
7.2 • Solutions 425 17. [M] The matrix of the quadratic form is 0619/2 609/21 A = ⎢ ⎥ ⎢ ⎥ − ⎢ ⎥ ⎣ ⎦ The eigenvalues of A are 19/2 0 6 9/2 1 6 0 . − […]
Education Chapter 8 Homework Then, since B is convex, Theorem 7 implies that B contains all convex
The Geometry of Vector Spaces 8.1 SOLUTIONS Notes . This section introduces a special kinds of linear combination used to describe the sets created when a subspace is shifted away from the origin. An affine combination is a linear combination […]
Education Chapter 8 Homework The weights sum to one, so this is an affine sum
8.4 • Solutions 467 h(t) = (1 − t) 3 p 0 + 3t(1 − t) 2 p 1 + 3t 2 (1 − t)p 2 + t 3 p 3 for 0 ≤ t ≤ 1 Thus, h(t) is […]
Education Maple Manual Homework Bezier Curve Degrees Amp Backward Gauss Uses
INSTRUCTOR’S MAPLE MANUAL DOUGLAS MEADE University of South Carolina LINEAR ALGEBRA AND ITS APPLICATIONS FOURTH EDITION David C. Lay University of Maryland The author and publisher of this book have used their best efforts in preparing this book. These efforts […]
Education Maple Manual Homework Example Verify That Matrix The Adjacency Matrix
3. Let A = [v1v2. . . vk] be a matrix whose columns are v1,v2, . . . , vk. Explain why the 4. Explain why the set of columns of A could not be linearly independent if A has […]
Education Maple Manual Homework Label Reference Repeating This Process Unchecks The
COMPUTER PROJECTS 17 Chapter 4: Space Flight and Control Systems This case study studies a mathematical model for engineering control systems. The central idea is that the rank of a matrix determines if a system is controllable. A system of […]
Education Maple Manual Homework Use Maple Find The Reduced Echelon Form
Maple Project: Temperature Distributions NameMaple Project: Temperature Distributions NameMaple Project: Temperature Distributions Name Purpose Given the temperature on a region’s boundary, determine the steady- state temperature inside. Prerequisites Section 2.5 Maple commands used IdentityMatrix and MatrixInverse from the LinearAlgebra pack- […]
Education Maple Manual Homework What Trends The Three Age Groups Are
3. The five matrices (A, B, C, D, and E ) can be loaded into a Maple session with the command: cxeigdat( );. Recall that the Maple name for matrix D is DD. The eigenvectors command can be used to […]
Education Matlab Homework Assume X and Y are sizes for which A11 X and
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 2. (hand) Using the matrices in question 1: (a) Can you calculate AC as 11 11 21 12 31 13 11 21 21 22 31 23 11 31 21 32 […]
Education Matlab Homework Elementary Analysis of the Spotted Owl Population
*It is suggested that this project not be assigned until after Section 1.5 or 1.6. MATLAB PROJECTS to accompany the text LINEAR ALGEBRA AND ITS APPLICATIONS, 4th ed., David C. Lay Title of Project Prerequisite Sections in Text Getting Started […]
Education Matlab Homework Only That One Best Choice Will Counted
INSTRUCTOR’S MATLAB® MANUAL JEREMY R. CASE Taylor University JANE DAY San Jose State University LINEAR ALGEBRA AND ITS APPLICATIONS FOURTH EDITION David C. Lay University of Maryland The author and publisher of this book have used their best efforts in […]
Education Matlab Homework Section 22 Note That Exercises And The
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 2. Now investigate products of lower triangular matrices which have all diagonal entries equal to 1. Such a matrix is called a unit lower triangular matrix. For example you could […]
Education Matlab Homework Use Draw Poly Sketch The Result Each Successive
Page 2 of 3 MATLAB Project: Reduced Echelon Form and ref 2. Let B = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡− 7.65.00 7.02.03.0 21.01.0 . (a) (hand) Calculate the reduced echelon form of B. Please show […]
Education Matlab Homework Verify the statements above for each matrix below
Page 5 of 5 MATLAB Project: Using Eigenvalues to Study Spotted Owls (c) Prove that the real eigenvalue 1 λ is greater than 23 |||| λλ =. Hence, the real positive eigenvalue of A will always be the dominant eigenvalue […]
Education Matlab Homework If you want to create a diary file, find where you will save the file
Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 4. Consider the sketch below. The standard unit square is shown on the left. (a) (hand) Find 33×matrices A, B and C so that applying your new matrices in succession […]