Linear Algebra with Applications (2-Download)
5th Edition
ISBN: 9780321796974
Author: Otto Bretscher
Publisher: PEARSON
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Chapter 1.3, Problem 4E
Find the rank of the matrices in Exercises 2 through 4.
4.
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Chapter 1 Solutions
Linear Algebra with Applications (2-Download)
Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...Ch. 1.1 - GOAL Set up and solve systems with as many as...
Ch. 1.1 - In Exercises 11 through 13,find all solutions of...Ch. 1.1 - In Exercises 11 through 13, find all solutions of...Ch. 1.1 - In Exercises 11 through 13, find all solutions of...Ch. 1.1 - In Exercises 14 through 16,find all solutions of...Ch. 1.1 - In Exercises 14 through 16, find all solutions of...Ch. 1.1 - In Exercises 14 through 16, find all solutions of...Ch. 1.1 - Find all solutions of the linear system | x+2y=a...Ch. 1.1 - Find all solutions of the linear system...Ch. 1.1 - Consider the linear system...Ch. 1.1 - Consider the linear system |x+yz=2x+2y+z=3x+y+( k...Ch. 1.1 - The sums of any two of three real numbers are 24,...Ch. 1.1 - Emile and Gertrude are brother and sister. Emile...Ch. 1.1 - Consider a two-commodity market. When the...Ch. 1.1 - The Russian-born U.S. economist and Nobel laureate...Ch. 1.1 - Find the outputs a andb needed to satisfy the...Ch. 1.1 - Consider the differential equation...Ch. 1.1 - Find all solutions of the system |7xy=x6x+8y=y| ,...Ch. 1.1 - On a sunny summer day, you are taking the...Ch. 1.1 - On your next trip to Switzerland, you should take...Ch. 1.1 - In a grid of wires, the temperature at exterior...Ch. 1.1 - Find the polynomial of degree 2 [a polynomial of...Ch. 1.1 - Find a polynomial of degree 2 [of the form...Ch. 1.1 - Find all the polynomials f(t) of degree 2 [of the...Ch. 1.1 - Find all the polynomials f(t) of degree 2 [of the...Ch. 1.1 - Find all the polynomials f(t) of degree 2 [of the...Ch. 1.1 - Find all the polynomials f(t) of degree 2 [of the...Ch. 1.1 - Find the function f(t) of the form f(t)=ae3t+be2t...Ch. 1.1 - Find the function f(t) of the form...Ch. 1.1 - Prob. 39ECh. 1.1 - Find the ellipse centered at the origin that runs...Ch. 1.1 - Find all points (a,b,c) in space for which the...Ch. 1.1 - Linear systems are particularly easy to solve when...Ch. 1.1 - Consider the linear system |x+y=1x+ t 2y=t| ,...Ch. 1.1 - Find a system of linear equations with three...Ch. 1.1 - Find a system of linear equations with three...Ch. 1.1 - Boris and Marina are shopping for chocolate bars....Ch. 1.1 - Here is another method to solve a system of linear...Ch. 1.1 - A hermit eats only two kinds of food: brown rice...Ch. 1.1 - I have 32 bills in my wallet, in the denominations...Ch. 1.1 - Some parking meters in Milan, Italy, accept coins...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - GOAL Use Gauss-Jordan elimination to solve linear...Ch. 1.2 - Solve the linear systems in Exercises 13 through...Ch. 1.2 - Solve the linear systems in Exercises 13 through...Ch. 1.2 - Solve the linear systems in Exercises 13 through...Ch. 1.2 - Prob. 16ECh. 1.2 - Solve the linear systems in Exercises 13 through...Ch. 1.2 - Determine which of the matrices below are in...Ch. 1.2 - Find all 41 matrices in reduced row-echelon form.Ch. 1.2 - For which values of a, b, c, d, and e is the...Ch. 1.2 - For which values of a, b, c, d, and e is the...Ch. 1.2 - We say that two nm matrices in reduced...Ch. 1.2 - How many types of 32 matrices in reduced...Ch. 1.2 - How many types of 23 matrices in reduced...Ch. 1.2 - Prob. 25ECh. 1.2 - Suppose matrix A is transformed into matrix B...Ch. 1.2 - Prob. 27ECh. 1.2 - Consider an nm in matrix A. Can you transform...Ch. 1.2 - Prob. 29ECh. 1.2 - Suppose you subtract a multiple of an equation in...Ch. 1.2 - Balancing a chemical reaction. Consider the...Ch. 1.2 - Find the polynomial of degree 3 [a polynomial of...Ch. 1.2 - Find the polynomial of degree 4 whose graph...Ch. 1.2 - Cubic splines. Suppose you are in charge of the...Ch. 1.2 - Find the polynomial f(t) of degree 3 such that...Ch. 1.2 - The dot product of two vectors x=[ x 1 x 2 x n]...Ch. 1.2 - Find all vectors in 4 that are perpendicular to...Ch. 1.2 - Find all solutions x1,x2,x3 of the equation...Ch. 1.2 - Prob. 39ECh. 1.2 - If we consider more than three industries in an...Ch. 1.2 - Consider the economy of Israel in 1958.11 The...Ch. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - The accompanying sketch represents a maze of...Ch. 1.2 - Let S(t) be the length of the tth day of the year...Ch. 1.2 - Prob. 46ECh. 1.2 - Consider the equations...Ch. 1.2 - Consider the equations |y+2kz=0x+2y+6z=2kx+2z=1| ,...Ch. 1.2 - a. Find all solutions x1,x2,x3,x4 of the system...Ch. 1.2 - For an arbitrary positive integer n3 , find all...Ch. 1.2 - Prob. 51ECh. 1.2 - Find all the polynomials f(t) of degree 3 such...Ch. 1.2 - Prob. 53ECh. 1.2 - Prob. 54ECh. 1.2 - Prob. 55ECh. 1.2 - Prob. 56ECh. 1.2 - Prob. 57ECh. 1.2 - Prob. 58ECh. 1.2 - Prob. 59ECh. 1.2 - Prob. 60ECh. 1.2 - Prob. 61ECh. 1.2 - Prob. 62ECh. 1.2 - Students are buying books for the new semester....Ch. 1.2 - Prob. 64ECh. 1.2 - At the beginning of a political science class at a...Ch. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - Prob. 72ECh. 1.2 - Pigeons are sold at the rate of 5 for 3 panas,...Ch. 1.2 - Prob. 74ECh. 1.2 - Prob. 75ECh. 1.2 - Prob. 76ECh. 1.2 - Prob. 77ECh. 1.2 - Prob. 78ECh. 1.2 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.3 - GOAL Use the reduced row-echelon form of the...Ch. 1.3 - Find the rank of the matrices in Exercises 2...Ch. 1.3 - Find the rank of the matrices in Exercises 2...Ch. 1.3 - Find the rank of the matrices in Exercises 2...Ch. 1.3 - a. Write the system |x+2y=73x+y=11| in vector...Ch. 1.3 - Consider the vectors v1,v2,v3 in 2 (sketched in...Ch. 1.3 - Consider the vectors v1,v2,v3 in 2 shown in the...Ch. 1.3 - Consider the vectors v1,v2,v3,v4 in 2 shown in...Ch. 1.3 - Write the system |x+2y+3z=14x+5y+6z=47x+8y+9z=9|...Ch. 1.3 - Compute the dot products in Exercises 10 through...Ch. 1.3 - Compute the dot products in Exercises 10 through...Ch. 1.3 - Compute the dot products in Exercises 10 through...Ch. 1.3 - Compute the products Axin Exercises 13 through 15...Ch. 1.3 - Compute the products Axin Exercises 13 through 15...Ch. 1.3 - Compute the products Axin Exercises 13 through 15...Ch. 1.3 - Compute the products Axin Exercises 16 through 19...Ch. 1.3 - Compute the products Axin Exercises 16 through 19...Ch. 1.3 - Compute the products Axin Exercises 16 through 19...Ch. 1.3 - Compute the products Axin Exercises 16 through 19...Ch. 1.3 - a. Find [234567]+[753101] . b. Find 9[112345] .Ch. 1.3 - Use technology to compute the product...Ch. 1.3 - Consider a linear system of three equations with...Ch. 1.3 - Consider a linear system of four equations with...Ch. 1.3 - Let A be a 44 matrix, and let b and c be two...Ch. 1.3 - Let A be a 44 matrix, and let b and c be two...Ch. 1.3 - Let A be a 43 matrix, and let b and c be two...Ch. 1.3 - If the rank of a 44 matrix A is 4, what is...Ch. 1.3 - If the rank of a 53 matrix A is 3, what is...Ch. 1.3 - In Problems 29 through 32, let x=[539]andy=[201]....Ch. 1.3 - In Problems 29 through 32, let x=[539]andy=[201]....Ch. 1.3 - In Problems 29 through 32, let x=[539]andy=[201]....Ch. 1.3 - In Problems 29 through 32, let x=[539]andy=[201]....Ch. 1.3 - Let A be the nn matrix with all 1‘s on the...Ch. 1.3 - We define the vectors e1=[001],e2=[010],e3=[001]...Ch. 1.3 - In m , we define ei=[0010]ithcomponent . If A is...Ch. 1.3 - Find a 33 matrix A such that...Ch. 1.3 - Find all vectors x such that Ax=b , where...Ch. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Consider an nm matrix A with more rows than...Ch. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - A linear system of the form Ax=0 is called...Ch. 1.3 - Consider a solution x1 of the linear system Ax=b...Ch. 1.3 - Consider the accompanying table. For some linear...Ch. 1.3 - Consider a linear system Ax=b , where A is a 43...Ch. 1.3 - Consider an nm matrix A, an rs matrix B, and...Ch. 1.3 - Consider the matrices A=[1012] and B=[0110] .Can...Ch. 1.3 - If A and B are two nm matrices, is (A+B)x=Ax+Bx...Ch. 1.3 - Prob. 54ECh. 1.3 - Prob. 55ECh. 1.3 - Is the vector [301385662] a linear combination of...Ch. 1.3 - Prob. 57ECh. 1.3 - For which values of the constants b and c is the...Ch. 1.3 - For which values of the constants c and d is...Ch. 1.3 - For which values of the constants a, b, c and d is...Ch. 1.3 - For which values of the constant c is [1cc2] a...Ch. 1.3 - For which values of the constant c is [1cc2] a...Ch. 1.3 - In Exercises 63 through 68, consider the vectors...Ch. 1.3 - In Exercises 63 through 68, consider the vectors...Ch. 1.3 - Prob. 65ECh. 1.3 - Prob. 66ECh. 1.3 - Prob. 67ECh. 1.3 - Prob. 68ECh. 1.3 - Prob. 69ECh. 1.3 - Let A be the nn matrix with 0’s on the main...Ch. 1 - TRUE OR FALSE? 19 Determine whether the statements...Ch. 1 - TRUE OR FALSE? 19 Determine whether the statements...Ch. 1 - Matrix [120001000] is in reduced row-echelon form.Ch. 1 - A system of four linear equations in three...Ch. 1 - There exists a 34 matrix with rank 4.Ch. 1 - If A is a 34 matrix and vector v is in 4 , then...Ch. 1 - If the 44 matrix A has rank 4, then any linear...Ch. 1 - There exists a system of three linear equations...Ch. 1 - There exists a 55 matrix A of rank 4 such that the...Ch. 1 - If matrix A is in reduced row-echelon form, then...Ch. 1 - The system [123456000]x=[123] is inconsistent.Ch. 1 - There exists 22 matrix A such that A=[12]=[34] .Ch. 1 - If A is a nonzero matrix of the form [abba] , then...Ch. 1 - rank [111123136]=3Ch. 1 - The system Ax=[0001] is inconsistent for all 43...Ch. 1 - There exists a 22 matrix A such that A=[11]=[12]...Ch. 1 - rank [222222222]=2Ch. 1 - [111315171921][131]=[131921]Ch. 1 - There exists a matrix A such that A=[12]=[357] .Ch. 1 - Vector [123] is a linear combination of vectors...Ch. 1 - If the system Ax=b has a unique solution, then...Ch. 1 - If A is any 43 matrix, then there exists a vector...Ch. 1 - There exist scalars a and b such that matrix...Ch. 1 - If v and w are vectors in 4 , then v must be a...Ch. 1 - If u,v , and w are nonzero vectors in 2 , then w...Ch. 1 - If v and w are vectors in 4 , then the zero vector...Ch. 1 - If A and B are any two 33 matrices of rank2,then...Ch. 1 - If vector u is a linear combination of vectors v...Ch. 1 - A linear system with fewer unknowns than...Ch. 1 - The rank of any upper triangular matrix is the...Ch. 1 - There exists a 43 matrix A of rank 3 such that...Ch. 1 - The system Ax=b is inconsistent if (and only...Ch. 1 - If A is a 43 matrix of rank 3 and Au=Aw for two...Ch. 1 - If A is a 44 matrix and the system Ax=[2345] has...Ch. 1 - If vector u is a linear combination of vectors v...Ch. 1 - If A=[uvw] and rref(A)=[002013000] , then the...Ch. 1 - If A and B are matrices of the same size, then the...Ch. 1 - If A and B are any two nn matrices of rank n, then...Ch. 1 - If a vector v in 4 is a linear combination of u...Ch. 1 - If matrix E is in reduced row-echelon form, and if...Ch. 1 - The linear system Ax=b consistent if (and only if)...Ch. 1 - If A is a 34 matrix of rank 3, then the system...Ch. 1 - If two matrices A and B have the same reduced...Ch. 1 - If matrix E is in reduced row-echelon form, and if...Ch. 1 - If A and B are two 22 matrices such that the...Ch. 1 - A lower triangular 33 matrix has rank 3 if (and...Ch. 1 - If adbc0 , then the matrix [abcd] must have rank...Ch. 1 - If vector w is a linear combination of u and v ,...Ch. 1 - If the linear system Ax=b has a unique solution...Ch. 1 - A matrix is called a 0-1-matrix if all of its...
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- ma Classes Term. Spring 2025 Title Details Credit Hours CRN Schedule Type Grade Mode Level Date Status Message *MATHEMATICS FOR MANAGEME... MTH 245, 400 4 54835 Online Normal Grading Mode Ecampus Undergradu... 03/21/2025 Registered **Web Registered... *SOIL SCIENCE CSS 205, 400 0 52298 Online Normal Grading Mode Undergraduate 03/21/2025 Waitlisted Waitlist03/21/2025 PLANT PATHOLOGY BOT 451, 400 4 56960 Online Normal Grading Mode Undergraduate 03/21/2025 Registered **Web Registered... Records: 3 Schedule Schedule Detailsarrow_forwardHere is an augmented matrix for a system of equations (three equations and three variables). Let the variables used be x, y, and z: 1 2 4 6 0 1 -1 3 0 0 1 4 Note: that this matrix is already in row echelon form. Your goal is to use this row echelon form to revert back to the equations that this represents, and then to ultimately solve the system of equations by finding x, y and z. Input your answer as a coordinate point: (x,y,z) with no spaces.arrow_forward1 3 -4 In the following matrix perform the operation 2R1 + R2 → R2. -2 -1 6 After you have completed this, what numeric value is in the a22 position?arrow_forward
- 5 -2 0 1 6 12 Let A = 6 7 -1 and B = 1/2 3 -14 -2 0 4 4 4 0 Compute -3A+2B and call the resulting matrix R. If rij represent the individual entries in the matrix R, what numeric value is in 131? Input your answer as a numeric value only.arrow_forward1 -2 4 10 My goal is to put the matrix 5 -1 1 0 into row echelon form using Gaussian elimination. 3 -2 6 9 My next step is to manipulate this matrix using elementary row operations to get a 0 in the a21 position. Which of the following operations would be the appropriate elementary row operation to use to get a 0 in the a21 position? O (1/5)*R2 --> R2 ○ 2R1 + R2 --> R2 ○ 5R1+ R2 --> R2 O-5R1 + R2 --> R2arrow_forwardThe 2x2 linear system of equations -2x+4y = 8 and 4x-3y = 9 was put into the following -2 4 8 augmented matrix: 4 -3 9 This augmented matrix is then converted to row echelon form. Which of the following matrices is the appropriate row echelon form for the given augmented matrix? 0 Option 1: 1 11 -2 Option 2: 4 -3 9 Option 3: 10 ܂ -2 -4 5 25 1 -2 -4 Option 4: 0 1 5 1 -2 Option 5: 0 0 20 -4 5 ○ Option 1 is the appropriate row echelon form. ○ Option 2 is the appropriate row echelon form. ○ Option 3 is the appropriate row echelon form. ○ Option 4 is the appropriate row echelon form. ○ Option 5 is the appropriate row echelon form.arrow_forward
- Let matrix A have order (dimension) 2x4 and let matrix B have order (dimension) 4x4. What results when you compute A+B? The resulting matrix will have dimensions of 2x4. ○ The resulting matrix will be a single number (scalar). The resulting matrix will have dimensions of 4x4. A+B is undefined since matrix A and B do not have the same dimensions.arrow_forwardIf -1 "[a446]-[254] 4b = -1 , find the values of a and b. ○ There is no solution for a and b. ○ There are infinite solutions for a and b. O a=3, b=3 O a=1, b=2 O a=2, b=1 O a=2, b=2arrow_forwardA student puts a 3x3 system of linear equations is into an augmented matrix. The student then correctly puts the augmented matrix into row echelon form (REF), which yields the following resultant matrix: -2 3 -0.5 10 0 0 0 -2 0 1 -4 Which of the following conclusions is mathematically supported by the work shown about system of linear equations? The 3x3 system of linear equations has no solution. ○ The 3x3 system of linear equations has infinite solutions. The 3x3 system of linear equations has one unique solution.arrow_forward
- Solve the following system of equations using matrices: -2x + 4y = 8 and 4x - 3y = 9 Note: This is the same system of equations referenced in Question 14. If a single solution exists, express your solution as an (x,y) coordinate point with no spaces. If there are infinite solutions write inf and if there are no solutions write ns in the box.arrow_forwardI need help explaining on this examplearrow_forwardConsider the table of values below. x y 2 64 3 48 4 36 5 27 Fill in the right side of the equation y= with an expression that makes each ordered pari (x,y) in the table a solution to the equation.arrow_forward
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