5th Edition

ISBN: 9780321796943

Author: BRETSCHER, Otto.

Publisher: Pearson Education

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Chapter 1.2, Problem 11E

GOAL Use Gauss-Jordan elimination to solve linear systems. Do simple problems using paper and pencil, and use technology to solve more complicated problems.

In Exercises 1 through 12, find all solutions of the equations with paper and pencil using Gauss-Jordan elimination. Show all your work.

11. | x 1 + 2 x 3 + 4 x 4 = − 8 x 2 − 3 x 3 − x 4 = 6 3 x 1 + 4 x 2 − 6 x 3 + 8 x 4 = 0 − x 2 + 3 x 3 + 4 x 4 = − 12 |

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Chapter 1.2, Problem 10E

Chapter 1.2, Problem 12E

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Chapter 1 Solutions

Linear Algebra With Applications

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. 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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. 38E Ch. 1.3 - Prob. 39E Ch. 1.3 - Prob. 40E Ch. 1.3 - Prob. 41E Ch. 1.3 - Prob. 42E Ch. 1.3 - Prob. 43E Ch. 1.3 - Consider an nm matrix A with more rows than...Ch. 1.3 - Prob. 45E Ch. 1.3 - Prob. 46E Ch. 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. 54E Ch. 1.3 - Prob. 55E Ch. 1.3 - Is the vector [301385662] a linear combination of...Ch. 1.3 - Prob. 57E Ch. 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. 65E Ch. 1.3 - Prob. 66E Ch. 1.3 - Prob. 67E Ch. 1.3 - Prob. 68E Ch. 1.3 - Prob. 69E Ch. 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]=3 Ch. 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]=2 Ch. 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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