Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 6.3, Problem 1E
Find the area of the parallelogram defined by
Expert Solution & Answer
Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video
schedule00:47
Students have asked these similar questions
(a)
(b)
(c)
(d)
de
unique?
Answer the following questions related to the linear system
x + y + z = 2
x-y+z=0
2x + y 2 3
rewrite the linear system into the matrix-vector form A = 5
Fuse elementary row operation to solve this linear system. Is the solution
use elementary row operation to find the inverse of A and then solve
the linear system. Verify the solution is the same as (b).
give the null space of matrix A and find the dimension of null space.
give the column space of matrix A and find the dimension of the column
space of A (Hint: use Rank-Nullity Theorem).
please explain in a clear way
Solve questions by Course Name Ordinary Differential Equations
Chapter 6 Solutions
Linear Algebra with Applications (2-Download)
Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...
Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 11 through 22, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - In Exercises 23 through 30, use the determinant to...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - Find the determinants of the matrices A in...Ch. 6.1 - If A is an nn matrix, what is the relationship bet...Ch. 6.1 - If A is an nn matrix and k is an arbitrary...Ch. 6.1 - If A is a 22 matrix, what is the relationship...Ch. 6.1 - If A is an invertible 22 matrix, what is the...Ch. 6.1 - Find nonzero numbers a, b, c, d, e, f, g, h such...Ch. 6.1 - Find 22 matrices A, B, C, D such that...Ch. 6.1 - For two nonparallel vectors v and w in 3 ,...Ch. 6.1 - Prob. 50ECh. 6.1 - Explain why any pattern P in a matrix A, other...Ch. 6.1 - Consider two vectors v and w in 3 . Form the...Ch. 6.1 - Find the determinant of the (2n)(2n) matrix A=[0 I...Ch. 6.1 - Is the determinant of the matrix...Ch. 6.1 - Does the following matrix have an LU...Ch. 6.1 - Let Mn be the nn matrix with all 1‘s along “the...Ch. 6.1 - A square matrix is called a permutation matrix if...Ch. 6.1 - a. Find a noninvertible 22 matrix whose entries...Ch. 6.1 - Consider the function F(A)=F[vw]=vw from 22 to ,...Ch. 6.1 - Which of the following functions F of A=[abcd] are...Ch. 6.1 - Show that the function F[abcdefghj]=bfg is linear...Ch. 6.1 - In Exercises 62 through 64, consider a function D...Ch. 6.1 - In Exercises 62 through 64, consider a function D...Ch. 6.1 - In Exercises 62 through 64, consider a function D...Ch. 6.1 - Consider a function D from 33 to that is linearin...Ch. 6.1 - a. Let V be the linear space of all functions F...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Use Gaussian elimination to find the determinant...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Consider a 44matrix A with rows v1,v2,v3,v4. If...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Find the determinants of the linear...Ch. 6.2 - Let Pn be the nn matrix whose entries are all...Ch. 6.2 - Consider two distinct real numbers, a and b. We...Ch. 6.2 - Vandermonde determinants (introduced by...Ch. 6.2 - Use Exercise 31 to find...Ch. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Consider two distinct points [a1a2] and [b1b2] in...Ch. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - If A is an invertible matrix, what can you say...Ch. 6.2 - If A is an orthogonal matrix, what are the...Ch. 6.2 - Consider a skew-symmetric nn matrix A. where nis...Ch. 6.2 - Consider an nm matrix A=QR ,where Q is an nm...Ch. 6.2 - Consider two vectors v and w in n . Form the...Ch. 6.2 - The cross product in n . Consider the vectors...Ch. 6.2 - Find the derivative of the function...Ch. 6.2 - Given some numbers a, b, c, d, e, and f such that...Ch. 6.2 - Is the function T[abcd]=ad+bc linear in the rows...Ch. 6.2 - Consider the linear transformation T(x)=det[ v 1...Ch. 6.2 - Give an example of a 33 matrix A with all nonzero...Ch. 6.2 - Find the determinant of the matrix...Ch. 6.2 - Find the determinant of the (2n)(2n) matrix A=[0 I...Ch. 6.2 - Consider a 22 matrix A=[abcd] with column vectors...Ch. 6.2 - Consider an invertible 22 matrix A with...Ch. 6.2 - Let A and B be 22 matrices with integer entries...Ch. 6.2 - For a fixed positive integer n, let D be a...Ch. 6.2 - Use the characterization of the determinant given...Ch. 6.2 - Consider a linear transformation T from m+n to m...Ch. 6.2 - Find the matrix M introduced in Exercise 57for the...Ch. 6.2 - If the equation detA=detB holds for two nn...Ch. 6.2 - Consider an nn matrix A. Show that swapping the...Ch. 6.2 - Consider nn matrices A. B. C, and D, where A...Ch. 6.2 - Consider nn matrices A, B , C, and D such that...Ch. 6.2 - Show that more than n!=123n multiplications are...Ch. 6.2 - Show that fewer than en! algebraic operations...Ch. 6.2 - Let Mn be the nn matrix with 1‘s on the main...Ch. 6.2 - Let Mn be the matrix with all 1‘s along the main...Ch. 6.2 - Consider a pattern P in an nn matrix, and choose...Ch. 6.2 - Using the terminology introduced in the proof of...Ch. 6.2 - Let G be the set of all integers x that can be...Ch. 6.2 - Throughout this exercise, consider the Fibonacci...Ch. 6.3 - Find the area of the parallelogram defined by [37]...Ch. 6.3 - Find the area of the triangle defined by [37] and...Ch. 6.3 - Prob. 3ECh. 6.3 - Consider the area A of the triangle with vertices...Ch. 6.3 - The tetrahedron defined by three vectors v1,v2,v3...Ch. 6.3 - What is the relationship between the volume of...Ch. 6.3 - Find the area of the following region:Ch. 6.3 - Demonstrate the equation |detA|=v1v2vn for a...Ch. 6.3 - If v1 and v2 are linearly independent vectors in 2...Ch. 6.3 - Consider an nn matrix A=[v1v2vn] .What is the...Ch. 6.3 - Consider a linear transformation T(x)=Ax from 2 to...Ch. 6.3 - Consider those 44 matrices whose entries are all...Ch. 6.3 - Prob. 13ECh. 6.3 - Find the 3-volume of the 3-parallelepiped defined...Ch. 6.3 - Demonstrate Theorem 6.3.6 for linearly dependent...Ch. 6.3 - True orfalse? If is a parallelogram in 3 and...Ch. 6.3 - (For some background on the cross product in n ,...Ch. 6.3 - If T(x)=Ax is an invertible linear transformation...Ch. 6.3 - A basis v1,v2,v3 of 3 is called positively...Ch. 6.3 - We say that a linear transformation T from 3 to 3...Ch. 6.3 - Arguing geometrically, determine whether the...Ch. 6.3 - Use Cramer’s rule to solve the systems in...Ch. 6.3 - Use Cramer’s rule to solve the systems in...Ch. 6.3 - Use Cramer’s rule to solve the systems in...Ch. 6.3 - Find the classical adjoint of the matrix...Ch. 6.3 - Consider an nn matrix A with integer entries such...Ch. 6.3 - Consider two positive numbers a and b. Solve the...Ch. 6.3 - In an economics text,10 we find the following...Ch. 6.3 - In an economics text11 we find the following...Ch. 6.3 - Find the classical adjointof A=[100230456] .Ch. 6.3 - Find the classical adjointof A=[111123166] .Ch. 6.3 - Find the classical adjointof A=[0001010000101000]...Ch. 6.3 - Find the classical adjointof A=[1000020000300004]...Ch. 6.3 - For an invertible nn matrix A, find the product...Ch. 6.3 - For an invertible nn matrix A, what is the...Ch. 6.3 - For an invertible nn matrix A, what is adj(adj A)?Ch. 6.3 - For an invertible nn matrix A, what is the...Ch. 6.3 - For two invertible nn matrices A and B, what is...Ch. 6.3 - If A and B are invertible nn matrices, and if A...Ch. 6.3 - For an invertible nn matrix A. consider the...Ch. 6.3 - Show that an nn matrix A has at least one...Ch. 6.3 - Even if an nn matrix A fails to be invertible, we...Ch. 6.3 - Show that A(adjA)=0(adjA)A for all noninvertible...Ch. 6.3 - If A isan nn matrixo frank n1 , what is the rank...Ch. 6.3 - Find all 22 matrices A such that adj(A)=AT .Ch. 6.3 - (For those who have studied multivariable...Ch. 6.3 - Consider the quadrilateral in the accompanying...Ch. 6.3 - What is the area of the largest ellipse you can...Ch. 6.3 - What are the lengths of the semi axes of the...Ch. 6 - If B is obtained be multiplying a column of A by...Ch. 6 - det(A10)=(detA)10 for all 1010 matrices A.Ch. 6 - The determinant of any diagonal nn matrix is the...Ch. 6 - If matrix B is obtained by swapping two rows of an...Ch. 6 - If A=[uvw] is any 33 matrix, then detA=u(vw) .Ch. 6 - det(4A)=4detA for all 44 matrices A.Ch. 6 - det(A+B)=4detA+detB for all 55 matrices A and B.Ch. 6 - The equation det(A)=detA holds for all 66...Ch. 6 - If all the entries of a 77 matrix A are 7, then...Ch. 6 - An 88 matrix fails to be invertible if (and only...Ch. 6 - Prob. 11ECh. 6 - Prob. 12ECh. 6 - Prob. 13ECh. 6 - Prob. 14ECh. 6 - Prob. 15ECh. 6 - Prob. 16ECh. 6 - Prob. 17ECh. 6 - Prob. 18ECh. 6 - Prob. 19ECh. 6 - Prob. 20ECh. 6 - If all the entries of a square matrix are 1 or 0,...Ch. 6 - If all the entries of a square matrix A are...Ch. 6 - If all the columns of a square matrix A are unit...Ch. 6 - If A is any noninvertible square matrix, then...Ch. 6 - If the determinant of a square matrix is 1 , then...Ch. 6 - If all the entries of an invertible matrix A are...Ch. 6 - There exists a 44 matrix A whose entries are all 1...Ch. 6 - If the determinant of a 22 matrix A is 4, then the...Ch. 6 - If A=[uvw] is a 33 matrix, then the formula...Ch. 6 - There exist invertible 22 matrices A and B such...Ch. 6 - There exist real invertible 33 matrices A and S...Ch. 6 - There exist real invertible 33 matrices A and S...Ch. 6 - If A is any symmetric matrix, then detA=1 or...Ch. 6 - If A is any skew-symmetric 44 matrix, then detA=0...Ch. 6 - If detA=detB for two nn matrices A and B, thenA...Ch. 6 - Suppose A is an nn matrix and B is obtained fromA...Ch. 6 - If an nn matrix A is invertible, then there must...Ch. 6 - If all the entries of matrices A and A1 are...Ch. 6 - If a square matrix A is invertible, then its...Ch. 6 - There exists a real 33 matrix A such that A2=I3 .Ch. 6 - If all the diagonal entries of an nn matrix A are...Ch. 6 - If all the diagonal entries of nn matrix A are...Ch. 6 - For every nonzero 22 matrix A there exists a 22...Ch. 6 - If A is a 44 matrix whose entries are all 1 or 1 ,...Ch. 6 - If A is an invertible nn matrix, then A must...Ch. 6 - There exists a real number k such that the matrix...Ch. 6 - If A and B are orthogonal nn matrices such that...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Fill in each blank so that the resulting statement is true.
1. A combination of numbers, variables, and opera...
College Algebra (7th Edition)
In Exercises 5–12, find and sketch the domain for each function.
11.
University Calculus: Early Transcendentals (4th Edition)
Draining a tank An inverted conical water tank with a height of 12 ft and a radius of 6 ft is drained through a...
Calculus: Early Transcendentals (2nd Edition)
Sketch the graph of y= x . (p. 22)
Precalculus
If two fair dice are rolled, what is the conditional probability that the first one lands on 6 given that the ...
A First Course in Probability (10th Edition)
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
- Determine whether it's true or false and the reasoning is neededarrow_forward1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.arrow_forward5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}arrow_forward
- For the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)arrow_forwardQuestions 1. Identify and describe potential bias in the study. 2. Identify and describe the way in which the selected participants may or may not represent the population as a whole. 3. Identify and describe the possible problems with the end results since the majority will be from females rather than an even split. 4. Identify and describe the possible problems with identifying females as possibly more vulnerable based on the data collected. 5. Identify a possible null hypothesis and problems in how the study might address this null hypothesis. 6. Identify one possible method of improving the study design and describe how it would improve the validity of the conclusions. 7. Identify a second possible method of improving the study design and describe how it would improve the validity of the conclusions.arrow_forwardThe Course Name Real Analysis please Solve questions by Real Analysisarrow_forward
- part 3 of the question is: A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forward2. The duration of the ride is 15 min. (a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel? (b) What is the position of that passenger when the ride ends?arrow_forward3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents the pendulum's displacement as a function of time. Answer: f(t) (a) Write an equation to represent the displacement of the pendulum as a function of time. (b) Graph the function. 10 9 8 7 6 5 4 3 2 1 0 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -1 -5. -6 -7 -8 -9 -10-arrow_forward
- A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. (a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. (b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forwardThe Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward1. Graph the function f(x)=sin(x) −2¸ Answer: y -2π 一元 1 −1 -2 -3 -4+ 元 2πarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
An Introduction to Area | Teaching Maths | EasyTeaching; Author: EasyTeaching;https://www.youtube.com/watch?v=_uKKl8R1xBM;License: Standard YouTube License, CC-BY
Area of a Rectangle, Triangle, Circle & Sector, Trapezoid, Square, Parallelogram, Rhombus, Geometry; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=JnLDmw3bbuw;License: Standard YouTube License, CC-BY