Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x, y, and z as your variables, each representing the columns in turn.) 1 0 0 9 0 1 0 2 0 0 0 0 (a) Determine whether the system has a solution. The system has one solution.The system has infinitely many solutions. The system has no solution. (b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) (x, y, z) =
Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x, y, and z as your variables, each representing the columns in turn.) 1 0 0 9 0 1 0 2 0 0 0 0 (a) Determine whether the system has a solution. The system has one solution.The system has infinitely many solutions. The system has no solution. (b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) (x, y, z) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x, y, and z as your variables, each representing the columns in turn.)
|
0 | 0 | 9 |
|
||||
| 0 | 1 | 0 | 2 | |||||
| 0 | 0 | 0 | 0 |
(a) Determine whether the system has a solution.
(b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
The system has one solution.The system has infinitely many solutions. The system has no solution.
(b) Find the solution or solutions to the system, if they exist. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
(x, y, z) =
Expert Solution
Step 1
A matrix is said to be consistent and have a unique solution when the rank of the coefficient matrix and the augmented matrix is the same and is equal to the number of unknowns. But if it is less than the number of unknowns, then the system will have infinitely many solutions. Now finally if they are different then the system is inconsistent and has no solution.
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