
Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 4.3, Problem 43E
a.
To determine
To Find: the change of basis matrix
b.
To determine
To Prove: the formula
c.
To determine
To Find: the change of basis matrix
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Solve questions
Patterns in Floor Tiling A square floor is to be tiled with square tiles as shown. There are blue tiles on the main diagonals and red tiles everywhere else.
In all cases, both blue and red tiles must be used. and the two diagonals must have a common blue tile at the center of the floor.
If 81 blue tiles will be used, how many red tiles will be needed?
Find the values of n, if the points (n + 1, 2n), (3n, 2n + 3) and (5n + 1,5n) are collinear.
Find the value of k that the four points (4,1,2), (5, k, 6), (5,1,-1) and (7,4,0) are coplanar.
Find the value of r if the area of the triangle is formed by the points (-3,6),(4,4) and (r,-2) is
12 sq units.
Find the volume of tetrahedron whose vertices are A(1,1,0), B(-4,3,6), C(-1,0,3) and
D(2,4,-5).
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
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- - Consider the following system of linear equations in the variables a,b,c,d: 5a-3b 7c - 2d = 2 2ab 2c+ 5d = -3 → (*) 4a 3b 5d = 3 6a b+2c+ 7d = −7 (a) Solve the system (*) by using Gauss elimination method. (b) Solve the system (*) by using Cramer's rule method.arrow_forwardSolve for a 25 55 30 a=?arrow_forward9:41 … 93 Applying an Exponential Function to Newton's Law of Cooling 60. Water in a water heater is originally Aa ← 122°F. The water heater is shut off and the water cools to the temperature of the surrounding air, which is 60°F. The water cools slowly because of the insulation inside the heater, and the value of k is measured as 0.00351. a. Write a function that models the temperature T (t) (in °F) of the water t hours after the water heater is shut off. b. What is the temperature of the water 12 hr after the heater is shut off? Round to the nearest degree. c. Dominic does not like to shower with water less than 115°F. If Dominic waits 24 hr. will the water still be warm enough for a shower? Mixed Exercises ger-ui.prod.mheducation.comarrow_forward
- Please use the infinite series formula and specify how you did each step. Thank you.arrow_forward8) Solve the given system using the Gaussian Elimination process. 2x8y = 3 (-6x+24y = −6arrow_forward7) Solve the given system using the Gaussian Elimination process. (5x-4y = 34 (2x - 2y = 14arrow_forward
- 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.arrow_forwardUse 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.arrow_forwardH.w: Find the Eigen vectors for the largest Eigen value of the system X1+ +2x3=0 3x1-2x2+x3=0 4x1+ +3x3=0arrow_forward
- need 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_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher: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

Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning

Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Linear Transformations on Vector Spaces; Author: Professor Dave Explains;https://www.youtube.com/watch?v=is1cg5yhdds;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY