Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.2, Problem 24E
In Exercises 21 through 26, find a redundant column
24.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Listen
A falling object travels a distance given by the formula d = 6t + 9t2 where d is in feet
and t is the time in seconds. How many seconds will it take for the object to travel
112 feet? Round answer to 2 decimal places. (Write the number, not the units).
Your Answer:
Solve by the quadratic formula or completing the square to obtain exact solutions.
2
e
104
OA) -16±3√6
B) 8±√10
O c) -8±√10
OD) 8±3√√6
U
Question 14 (1 point)
Listen
The frame on a picture is 18 in by 22 in outside and is of uniform width. Using
algebraic methods, what is the width of the frame if the inner area of the picture
shown is 250 in²2? Write answer to 2 decimal places. (Write the number with no
units).
18 in
Your Answer:
22 in
Chapter 3 Solutions
Linear Algebra with Applications (2-Download)
Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...
Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - Describe the images and kernels of the...Ch. 3.1 - Prob. 24ECh. 3.1 - Describe the images and kernels of the...Ch. 3.1 - What is the image of a function f from to given...Ch. 3.1 - Give an example of a noninvertible function f from...Ch. 3.1 - Prob. 28ECh. 3.1 - Give an example of a function whose image is the...Ch. 3.1 - Give an example of a matrix A such that im(A)...Ch. 3.1 - Give an example of a matrix A such that im(A) is...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Consider a nonzero vector v in 3 . Arguing...Ch. 3.1 - Prob. 36ECh. 3.1 - For the matrix A=[010001000] , describe the images...Ch. 3.1 - Consider a square matrix A. a. What is the...Ch. 3.1 - Consider an np matrix A and a pm matrix B. a. What...Ch. 3.1 - Consider an np matrix A and a pm matrix B. If...Ch. 3.1 - Consider the matrix A=[0.360.480.480.64] . a....Ch. 3.1 - Express the image of the matrix...Ch. 3.1 - Prob. 43ECh. 3.1 - Consider a matrix A, and let B=rref(A) . a. Is...Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Consider a 22 matrix A with A2=A . a. If w is in...Ch. 3.1 - Verify that the kernel of a linear transformation...Ch. 3.1 - Consider a square matrix A with ker(A2)=ker(A3) ....Ch. 3.1 - Consider an np matrix A and a pm in matrix B...Ch. 3.1 - Prob. 52ECh. 3.1 - In Exercises 53 and 54, we will work with the...Ch. 3.1 - See Exercise 53 for some background. When...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Consider the vectors v1,v2,...,vm in n . Is span...Ch. 3.2 - Give a geometrical description of all subspaces of...Ch. 3.2 - Consider two subspaces V and W of n . a. Is the...Ch. 3.2 - Consider a nonempty subset W of n that is closed...Ch. 3.2 - Find a nontrivial relation among the following...Ch. 3.2 - Consider the vectors v1,v2,...,vm in n , with vm=0...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Prob. 33ECh. 3.2 - Consider the 54 matrix A=[ v 1 v 2 v 3 v 4] ....Ch. 3.2 - Prob. 35ECh. 3.2 - Consider a linear transformation T from n to p...Ch. 3.2 - Consider a linear transformation T from n to p...Ch. 3.2 - Prob. 38ECh. 3.2 - Consider some linearly independent vectors...Ch. 3.2 - Consider an np matrix A and a pm matrix B. Weare...Ch. 3.2 - Prob. 41ECh. 3.2 - Consider some perpendicular unit vectors...Ch. 3.2 - Consider three linearly independent vectors...Ch. 3.2 - Consider linearly independent vectors v1,v2,...,vm...Ch. 3.2 - Prob. 45ECh. 3.2 - Find a basis of the kernel of the matrix...Ch. 3.2 - Consider three linearly independent vectors...Ch. 3.2 - Express the plane V in 3 with equation...Ch. 3.2 - Express the line L in 3 spanned by the vector...Ch. 3.2 - Consider two subspaces V and W of n . Let V+W...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Consider a subspace V of n . We define the...Ch. 3.2 - Consider the line L spanned by [123] in 3 . Find a...Ch. 3.2 - Consider the subspace L of 5 spanned by the...Ch. 3.2 - Prob. 56ECh. 3.2 - Consider the matrix...Ch. 3.2 - Prob. 58ECh. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - Consider the matrices C=[ 1 1 1 1 0 0 1 1 1],H=[ 1...Ch. 3.3 - Determine whether the following vectors form a...Ch. 3.3 - For which value(s) of the constant k do the...Ch. 3.3 - Find a basis of the subspace of 3 defined by...Ch. 3.3 - Find a basis of the subspace of 4 defined by the...Ch. 3.3 - Let V be the subspace of 4 defined by the equation...Ch. 3.3 - Find a basis of the subspace of 4 that consists of...Ch. 3.3 - A subspace V of n is called a hyperplane if V...Ch. 3.3 - Consider a subspace V in m that is defined by...Ch. 3.3 - Consider a nonzero vector v in n . What is the...Ch. 3.3 - Can you find a 33 matrix A such that im(A)=ker(A)...Ch. 3.3 - Give an example of a 45 matrix A with dim(kerA)=3...Ch. 3.3 - a. Consider a linear transformation T from 5 to 3...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - In Exercises 40 through 43, consider the problem...Ch. 3.3 - Prob. 43ECh. 3.3 - For Exercises 44 through 61, consider the problem...Ch. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - For Exercises 44 through 61, consider the problem...Ch. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Find all points P in the plane such that you can...Ch. 3.3 - Prob. 62ECh. 3.3 - Consider two subspaces V and W of n , where Vis...Ch. 3.3 - Consider a subspace V of n with dim(V)=n . Explain...Ch. 3.3 - Consider two subspaces V and W of n , with VW={0}...Ch. 3.3 - Two subspaces V and W of n arc called...Ch. 3.3 - Consider linearly independent vectors v1,v2,...vp...Ch. 3.3 - Use Exercise 67 to construct a basis of 4 that...Ch. 3.3 - Consider two subspaces V and W of n . Show that...Ch. 3.3 - Use Exercise 69 to answer the following question:...Ch. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Consider the matrix A=[1221] . Find scalars...Ch. 3.3 - Prob. 77ECh. 3.3 - An nn matrix A is called nilpotent if Am=0 for...Ch. 3.3 - Consider a nilpotent nn matrix A. Use the...Ch. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - If a 33 matrix A represents the projection onto a...Ch. 3.3 - Consider a 42 matrix A and a 25 matrix B. a. What...Ch. 3.3 - Prob. 84ECh. 3.3 - Prob. 85ECh. 3.3 - Prob. 86ECh. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Prob. 90ECh. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - Prob. 40ECh. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - Consider the plane x1+2x2+x3=0 with basis...Ch. 3.4 - Consider the plane 2x13x2+4x3=0 with basis...Ch. 3.4 - Consider the plane 2x13x2+4x3=0. Find a basis of...Ch. 3.4 - Consider the plane x1+2x2+x3=0. Find a basis of...Ch. 3.4 - Consider a linear transformation T from 2 to 2...Ch. 3.4 - In the accompanying figure, sketch the vector x...Ch. 3.4 - Prob. 49ECh. 3.4 - Given a hexagonal tiling of the plane, such as you...Ch. 3.4 - Prob. 51ECh. 3.4 - If is a basis of n , is the transformation T from...Ch. 3.4 - Consider the basis of 2 consisting of the vectors...Ch. 3.4 - Let be the basis of n consisting of the vectors...Ch. 3.4 - Consider the basis of 2 consisting of the vectors...Ch. 3.4 - Find a basis of 2 such that andCh. 3.4 - Show that if a 33 matrix A represents the...Ch. 3.4 - Consider a 33 matrix A and a vector v in 3...Ch. 3.4 - Is matrix [2003] similar to matrix [2113] ?Ch. 3.4 - Is matrix [1001] similar to matrix [0110] ?Ch. 3.4 - Find a basis of 2 such that the matrix of the...Ch. 3.4 - Find a basis of 2 such that the matrix of the...Ch. 3.4 - Prob. 63ECh. 3.4 - Is matrix [abcd] similar to matrix [acbd] for all...Ch. 3.4 - Prove parts (a) and (b) of Theorem 3.4.6.Ch. 3.4 - Consider a matrix A of the form A=[abba] , where...Ch. 3.4 - If c0 ,find the matrix of the linear...Ch. 3.4 - Prob. 68ECh. 3.4 - If A is a 22 matrix such that A[12]=[36] and...Ch. 3.4 - Is there a basis of 2 such that matrix B of...Ch. 3.4 - Suppose that matrix A is similar to B, with B=S1AS...Ch. 3.4 - If A is similar to B, what is the relationship...Ch. 3.4 - Prob. 73ECh. 3.4 - Consider the regular tetrahedron in the...Ch. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - This problem refers to Leontief’s input—output...Ch. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Consider the linear transformation...Ch. 3.4 - Prob. 82ECh. 3 - If v1,v2,...,vn and w1,w2,...,wm are any twobases...Ch. 3 - If A is a 56 matrix of rank 4, then the nullity of...Ch. 3 - The image of a 34 matrix is a subspace of 4 .Ch. 3 - The span of vectors v1,v2,...,vn consists of all...Ch. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - The kernel of any invertible matrix consists of...Ch. 3 - The identity matrix In is similar to all...Ch. 3 - Prob. 9ECh. 3 - The column vectors of a 54 matrix must be...Ch. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Vectors [100],[210],[321] form a basis of 3 .Ch. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - If a 22 matrix P represents the orthogonal...Ch. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - If A and B are nn matrices, and vector v is in...Ch. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 41ECh. 3 - If two nn matrices A and B have the same rank,...Ch. 3 - Prob. 43ECh. 3 - If A2=0 for a 1010 matrix A, then the inequality...Ch. 3 - Prob. 45ECh. 3 - Prob. 46ECh. 3 - Prob. 47ECh. 3 - Prob. 48ECh. 3 - Prob. 49ECh. 3 - Prob. 50ECh. 3 - Prob. 51ECh. 3 - Prob. 52ECh. 3 - Prob. 53E
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
- ◄ Listen A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 560 square feet. Find the width of the walkway (x) if the garden measures 15 feet wide by 19 feet long. Write answer to 2 decimal places. (Write the number without units). X 15 feet Your Answer: 19 feet Xarrow_forwardListen A stuntman jumps from a roof 440 feet from the ground. How long will it take him to reach the ground? Use the formula, distance, d = 16t2, (where t is in seconds). Write answer to 1 decimal place. (Write the number, not the units). Your Answer:arrow_forwardSolve x² - 10x + 24 = 0 ○ A) 4,6 B) -12, -2 C) 12,2 D) -4, -6arrow_forward
- Factor the polynomial completely. x^2- 9 A) (x - 1)(x -9) B) (x - 3)(x + 3) c) (x -3)(x-3) D) (x + 3)(x + 3)arrow_forwardDirections: Use the equation A = Pet to answer each question and be sure to show all your work. 1. If $5,000 is deposited in an account that receives 6.1% interest compounded continuously, how much money is in the account after 6 years? 2. After how many years will an account have $12,000 if $6,000 is deposited, and the account receives 3.8% interest compounded continuously? 3. Abigail wants to save $15,000 to buy a car in 7 years. If she deposits $10,000 into an account that receives 5.7% interest compounded continuously, will she have enough money in 7 years? 4. Daniel deposits $8,000 into a continuously compounding interest account. After 18 years, there is $13,006.40 in the account. What was the interest rate? 5. An account has $26,000 after 15 years. The account received 2.3% interest compounded continuously. How much was deposited initially?arrow_forwardTRIANGLES INDEPENDENT PRACTICE ription Criangle write and cow Using each picture or description of triangle write and solve an equation in ordering the number of degrees in each angle TRIANGLE EQUATION & WORK ANGLE MEASURES A B -(7x-2)° (4x) (3x)° (5x − 10) C (5x – 2) (18x) E 3. G 4. H (16x)° LL 2A= 2B= ZE=arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
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 IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher: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,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Vector Spaces | Definition & Examples; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=72GtkP6nP_A;License: Standard YouTube License, CC-BY
Understanding Vector Spaces; Author: Professor Dave Explains;https://www.youtube.com/watch?v=EP2ghkO0lSk;License: Standard YouTube License, CC-BY