Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 4.1, Problem 48E
To determine
To find: If
Justify your answer carefully.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
7) Solve the given system using the Gaussian Elimination process.
(5x-4y = 34
(2x - 2y = 14
33
(a)
(b)
Let
A(t) =
=
et
0
0
0 cos(t) sin(t)
0-sin(t) cos(t))
For any fixed tЄR, find det(A(t)).
Show that the matrix A(t) is invertible for any tЄ R, and find the
inverse (A(t))¹.
Use the infinite geometric sum to convert .258 (the 58 is recurring, so there is a bar over it) to a ratio of two integers. Please go over the full problem, specifying how you found r. Thank you.
Chapter 4 Solutions
Linear Algebra with Applications (2-Download)
Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - GOAL Find a basis of a linear space and thus...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...
Ch. 4.1 - Which of the subsets V of 33given in Exercises 6...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Let V be the space of all infinite sequences of...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 31ECh. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 33ECh. 4.1 - Find a basis for each of the spaces V in Exercises...Ch. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - If c is any vector in n , what are the possible...Ch. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - In the linear space of infinite sequences,...Ch. 4.1 - A function f(t) from to is called even if...Ch. 4.1 - Prob. 48ECh. 4.1 - Let L(m,n) be the set of all linear...Ch. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Make up a second-order linear DE whose solution...Ch. 4.1 - Show that in an n-dimensional linear space we can...Ch. 4.1 - Show that if W is a subspace of an n-dimensional...Ch. 4.1 - Show that the space F(,) of all functions from to...Ch. 4.1 - Show that the space of infinite sequences of real...Ch. 4.1 - We say that a linear space V is finitely generated...Ch. 4.1 - In this exercise we will show that the functions...Ch. 4.1 - Show that if 0 is the neutral element of a linear...Ch. 4.1 - Consider the sequence (f0,f1,f2) recursively...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 15ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 21ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 35ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 41ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 46ECh. 4.2 - Find out which of the transformations in Exercises...Ch. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Find the image, rank, kernel, and nullity of the...Ch. 4.2 - Find the kernel and nullity of the transformation...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - For the transformation T in Exercise 23, find the...Ch. 4.2 - For the transformation T in Exercise 42, find the...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Find the image and kernel of the transformation T...Ch. 4.2 - Define an isomorphism from P3 to 3 , if you can.Ch. 4.2 - Define an isomorphism from P3 to 22 , if you can.Ch. 4.2 - We will define a transformation T from nm to...Ch. 4.2 - Find the kernel and nullity of the linear...Ch. 4.2 - For which constants k is the linear transformation...Ch. 4.2 - For which constants k is the linear transformation...Ch. 4.2 - If matrix A is similar to B, is T(M)=AMMB an...Ch. 4.2 - For which real numbers co, c0,c1,...,cn is the...Ch. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - In Exercises 72 through 74, let Znbe the set of...Ch. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Let + be the set of positive real numbers. On + we...Ch. 4.2 - Prob. 79ECh. 4.2 - Prob. 80ECh. 4.2 - Prob. 81ECh. 4.2 - Prob. 82ECh. 4.2 - Consider linear transformations T from V to W and...Ch. 4.2 - Prob. 84ECh. 4.3 - GOAL Use the concept of coordinates. Find the...Ch. 4.3 - GOAL Use the concept of coordinates. Find the...Ch. 4.3 - Do the polynomials...Ch. 4.3 - Consider the polynomials f(t)=t+1 and...Ch. 4.3 - Prob. 5ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 21ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 32ECh. 4.3 - In Exercises 5 through 40, find the matrix of the...Ch. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - Prob. 45ECh. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - a. Find the change of basis matrix S from the...Ch. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - In Exercises 48 through 53, let V be the space...Ch. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - In Exercises 54 through 58, let V be the plane...Ch. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Consider a linear transformation T from V to V...Ch. 4.3 - In the plane V defined by the equation 2x1+x22x3=0...Ch. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Let V be the space of all upper triangular 22...Ch. 4.3 - Let V be the subspace of 22 spanned by the...Ch. 4.3 - Prob. 66ECh. 4.3 - Let V be the linear space of all functions of the...Ch. 4.3 - Consider the linear space V of all infinite...Ch. 4.3 - Consider a basis f1,...,fn , of Pn1.Let a1,...,an...Ch. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - In all parts of this problem, let V be the set of...Ch. 4.3 - Prob. 73ECh. 4 - The polynomials of degree less than 7 form a seven...Ch. 4 - Prob. 2ECh. 4 - Prob. 3ECh. 4 - Prob. 4ECh. 4 - The space 23 is five-dimensional.Ch. 4 - Prob. 6ECh. 4 - Prob. 7ECh. 4 - Prob. 8ECh. 4 - If W1 and W2 are subspaces of a linear space V,...Ch. 4 - If T is a linear transformation from P6 to 22 ,...Ch. 4 - Prob. 11ECh. 4 - Prob. 12ECh. 4 - Prob. 13ECh. 4 - All linear transformations from P3 to 22 are...Ch. 4 - If T is a linear transformation from V to V, then...Ch. 4 - Prob. 16ECh. 4 - Every polynomial of degree 3 can be expressed as a...Ch. 4 - a linear space V can be spanned by 10 elements,...Ch. 4 - Prob. 19ECh. 4 - There exists a 22 matrix A such that the space V...Ch. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - Prob. 30ECh. 4 - If W is a subspace of V, and if W is finite...Ch. 4 - Prob. 32ECh. 4 - Prob. 33ECh. 4 - Prob. 34ECh. 4 - Prob. 35ECh. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - Prob. 38ECh. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - The transformation D(f)=f from C to C is an...Ch. 4 - If T is a linear transformation from P4 to W with...Ch. 4 - The kernel of the linear transformation...Ch. 4 - If T is a linear transformation from V to V, then...Ch. 4 - If T is a linear transformation from P6 to P6 that...Ch. 4 - There exist invertible 22 matrices P and Q such...Ch. 4 - There exists a linear transformation from P6 to ...Ch. 4 - If f1,f2,f3 is a basis of a linear space V, and if...Ch. 4 - There exists a two-dimensional subspace of 22...Ch. 4 - The space P11 is isomorphic to 34 .Ch. 4 - If T is a linear transformation from V to W, and...Ch. 4 - If T is a linear transformation from V to 22 with...Ch. 4 - The function T(f(t))=ddt23t+4f(x)dx from P5 to P5...Ch. 4 - Any four-dimensional linear space has infinitely...Ch. 4 - If the matrix of a linear transformation T (with...Ch. 4 - If the image of a linear transformation T is...Ch. 4 - There exists a 22 matrix A such that the space of...Ch. 4 - If A, B, C, and D are noninvertible 22 matrices,...Ch. 4 - There exist two distinct three-dimensional...Ch. 4 - the elements f1,...,fn , (where f10 ) are linearly...Ch. 4 - There exists a 33 matrix P such that the linear...Ch. 4 - If f1,f2,f3,f4,f5 are elements of a linear space...Ch. 4 - There exists a linear transformation T from P6 to...Ch. 4 - If T is a linear transformation from V to W, and...Ch. 4 - If the matrix of a linear transformation T (with...Ch. 4 - Every three-dimensional subspace of 22 contains at...
Knowledge Booster
Similar questions
- H.w: Find the Eigen vectors for the largest Eigen value of the system X1+ +2x3=0 3x1-2x2+x3=0 4x1+ +3x3=0arrow_forwardneed help with 5 and 6 pleasearrow_forward1) Given matrix A below, answer the following questions: a) What is the order of the matrix? b) What is the element a13? c) What is the element a₁₁? 4 -1arrow_forward
- [25 points] Given the vector let v = ER² and the collection of vectors ε = E-{)·()}-{☹) (9)} = {(A)·(9)}· B: = and C = · {(6)·(})}· answer the following question. (a) (b) (c) (d) (e) verify Verify is a basis for R² and find the coordinate [] of under ε. Verify B is a basis for R2 and find the coordinate []B of ʊ Verify C is a basis for R2 and find the coordinate []c of under ε. under ε. Find the change-of-basis matrix [I]+B from basis B to basis ε, and EE+BUB Find the change-of-basis matrix [I]B+ε from basis Ɛ to basis B, and verify [U]B= [] B+EVEarrow_forwardExplain the following terms | (a) linear span (b) dimension of vector space (c) linearly independent (d) linearly dependent (e) rank of matrix Aarrow_forward3. Let u = 3/5 √ = and = -4/5 -() Define V span{ū, }. (a) (b) (c) Show that {u, } is orthonormal and forms a basis for V. Explicitly compute Projy w. Explicitly give a non-zero vector in V+.arrow_forward
- Is 1.1 0.65 -3.4 0.23 0.4 -0.44 a basis for R3? You must explain your answer 0arrow_forwardFind the values of x and y in the following scalar multiplication. 8 2 x 1 3 || y = 9 LY_ Show Calculatorarrow_forwardA professor gives two types of quizzes, objective and recall. He plans to give at least 15 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a recall quiz 30 minutes. The professor would like a student to spend at least 5 hours total (300 minutes) preparing for these quizzes. It takes the professor 1 minute to grade an objective quiz, and 1.5 minutes to grade a recall type quiz. How many of each type of quiz should the professor give in order to minimize his grading time (why still meeting the other requirements outlined)?arrow_forward
- Table 15-21 shows the relative frequencies of the scores of a group of students on a philosophy quiz.Table 15-21 Score45678 Relative frequency7%11%19%24%39%arrow_forwardInstructions: Answer each question showing all work. 1. Out of 30 animals at a veterinarian clinic, 8 cats and 4 dogs have been vaccinated. 6 cats and 12 dogs are not yet vaccinated. Create a two-way frequency table to represent the data. 2. Convert the table from number 1 into a two-way relative frequency table. Instructions: Based on the tables created in questions 1 and 2 above, answer questions 3-7. 3. What percentage of cats from the total animals are vaccinated? 4. What is the relative frequency of dogs from the total animals that are not yet vaccinated? 5. What is the conditional frequency of cats that have not been vaccinated? 6. What is the marginal frequency of the total number of animals vaccinated? 7. What is the joint frequency of the cats that are vaccinated?arrow_forwardThe the high 3000arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,