Homework Answers
16.a) Here, the given system is consistent, since the system has solution.
From the augmented matrix we see that there are two variables and two independent equations, since the last row contains only zeros and first two rows are linearly independent.
So, the system of equations has unique solution.
b) Here, the given system is consistent, since the system has solution.
From the augmented matrix we see that there are four variables and three independent equations, since there are three linearly independent rows in the given matrix.
The system of equations has infinitely many solutions since the number of variables is greater than the number of equations.
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Exercises 15 and 16 use the notation of Example 1 for matrices in echelon form. Suppose...
In exercises 21-24 the given matrices are in reduced row echelon form (check this). Assume each...
In exercises 21-24 the given matrices are in reduced row echelon form (check this). Assume each matrix corresponds to a homogeneous linear system. Write down the system and determine the general solution. See Method (1.2.2) and Method (1.2.4). 21. 1 0-1 3 0 2 -2 23 1 0 0 0-1 0010-3 0001 4/
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
The following augmented matrix is in row echelon form and represents a linear system. Use back-substitution...
The following augmented matrix is in row echelon form and represents a linear system. Use back-substitution to solve the system if possible. 1 1-16 0 112 0 0 11 What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Simplify your answer. Type an ordered triple.) There are infinitely many solutions. The solution set is x. Type an ordered triple....
6. The reduced row echelon form of a system of linear equations is shown below. Write...
6. The reduced row echelon form of a system of linear equations is shown below. Write the system of equations corresponding to the given matrix. Use x, y, and z as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 41 41 0 1 3 2 Lo 0 0 0
(1 point) Convert the system 2 - 422 - 3x3 = 4 -3. + 10x +...
(1 point) Convert the system 2 - 422 - 3x3 = 4 -3. + 10x + 73 -16 to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions. Augmented matrix 11.-4,-3,41-3,10,7.-16]] Echelon form: [1,43,4),(0,1,1,2 Is the system consistent? yes Solution (21, 22, 23) = ( O O O O O O ) Help: To enter a matrix use [[ 11. For example, to...
The augmented matrix of a system of linear equations has the following reduced echelon form. Use...
The augmented matrix of a system of linear equations has the following reduced echelon form. Use it to find the general solution of the system of equations 0 0 1 0 0 0 1 0 0 0 0 -1 5 -4 3 0 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0
(1 point) Convert the system 2r 8r2 3r. 3 1 to an augmented matrix, Then reduce...
(1 point) Convert the system 2r 8r2 3r. 3 1 to an augmented matrix, Then reduce the svstem to echelon form and determine if the system is consistent, If the system in consistent, then find all solutions. Augmented matrix Echelon form s the system consistent? select Solution: (1, 2, T3) + S1. Help: To enter a matrix use [ ][ ]] For example, to enter the 2 x 3 matrix 2 3 6 5 you would type T1,2,31[6,5,41n, so each...
(1 point) Given that the matrix [ 3 - 94 01 4 0 -6 1 1-3...
(1 point) Given that the matrix [ 3 - 94 01 4 0 -6 1 1-3 -6 -36] is the augmented matrix for a linear system, use technology to perform the row operations needed to transform the matrix to reduced echelon form. Then determine if the system is consistent and if it is, find all solutions to the system. Reduced echelon form: Is the system consistent? select Solution: (21, 22, 23)=( Help: To enter a matrix use [[ ],[1] ....
Use Gaussian elimination to find a row echelon form (not reduced row echelon form) of the...
Use Gaussian elimination to find a row echelon form (not reduced row echelon form) of the augmented matrix for the following system, and then use it to determine for which value of a the following system has infinitely many solutions. x - 2y + 4z = 1 * +3y + z = -9 2x - 3y + az = 0
In exercises 21-24 the given matrices are in reduced row echelon form (check this). Assume each matrix corresponds to a homogeneous linear system. Write down the system and determine the general solution. See Method (1.2.2) and Method (1.2.4). 21. 1 0-1 3 0 2 -2 23 1 0 0 0-1 0010-3 0001 4/
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
The following augmented matrix is in row echelon form and represents a linear system. Use back-substitution to solve the system if possible. 1 1-16 0 112 0 0 11 What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is (Simplify your answer. Type an ordered triple.) There are infinitely many solutions. The solution set is x. Type an ordered triple....
6. The reduced row echelon form of a system of linear equations is shown below. Write the system of equations corresponding to the given matrix. Use x, y, and z as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. 1 0 41 41 0 1 3 2 Lo 0 0 0
(1 point) Convert the system 2 - 422 - 3x3 = 4 -3. + 10x + 73 -16 to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions. Augmented matrix 11.-4,-3,41-3,10,7.-16]] Echelon form: [1,43,4),(0,1,1,2 Is the system consistent? yes Solution (21, 22, 23) = ( O O O O O O ) Help: To enter a matrix use [[ 11. For example, to...
The augmented matrix of a system of linear equations has the following reduced echelon form. Use it to find the general solution of the system of equations 0 0 1 0 0 0 1 0 0 0 0 -1 5 -4 3 0 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0
(1 point) Convert the system 2r 8r2 3r. 3 1 to an augmented matrix, Then reduce the svstem to echelon form and determine if the system is consistent, If the system in consistent, then find all solutions. Augmented matrix Echelon form s the system consistent? select Solution: (1, 2, T3) + S1. Help: To enter a matrix use [ ][ ]] For example, to enter the 2 x 3 matrix 2 3 6 5 you would type T1,2,31[6,5,41n, so each...
(1 point) Given that the matrix [ 3 - 94 01 4 0 -6 1 1-3 -6 -36] is the augmented matrix for a linear system, use technology to perform the row operations needed to transform the matrix to reduced echelon form. Then determine if the system is consistent and if it is, find all solutions to the system. Reduced echelon form: Is the system consistent? select Solution: (21, 22, 23)=( Help: To enter a matrix use [[ ],[1] ....
Use Gaussian elimination to find a row echelon form (not reduced row echelon form) of the augmented matrix for the following system, and then use it to determine for which value of a the following system has infinitely many solutions. x - 2y + 4z = 1 * +3y + z = -9 2x - 3y + az = 0
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