Consider the homogeneous system of equations with coefficient matrix A = 9 2 -1 01-2 18 4 -4 [Recall: A homogeneous system is one where the right hand side of each equation is 0.] (a) State the number of unknown variables in the homogeneous system of equations. Number of Variables n = Rank r = (b) Determine the rank of A. (c) Use the results in parts (a) and (b) to determine the number of free variables (or parameters) in the general solution to the system of equations Number of Free Variables k =
Consider the homogeneous system of equations with coefficient matrix A = 9 2 -1 01-2 18 4 -4 [Recall: A homogeneous system is one where the right hand side of each equation is 0.] (a) State the number of unknown variables in the homogeneous system of equations. Number of Variables n = Rank r = (b) Determine the rank of A. (c) Use the results in parts (a) and (b) to determine the number of free variables (or parameters) in the general solution to the system of equations Number of Free Variables k =
Chapter7: Matrices And Determinants
Section: Chapter Questions
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Consider the homogeneous system of equations with coefficient matrix
| � = |
|
. |
[Recall: A homogeneous system is one where the right hand side of each equation is 0.]
(a) State the number of unknown variables in the homogeneous system of equations.
Number of Variables � =
(b) Determine the rank of �.
Rank � =
(c) Use the results in parts (a) and (b) to determine the number of free variables (or parameters) in the general solution to the system of equations.
Number of Free Variables � =
![Consider the homogeneous system of equations with coefficient matrix
A =
9 2-1
0 1 -2
18 4 -4
[Recall: A homogeneous system is one where the right hand side of each equation is 0.]
(a) State the number of unknown variables in the homogeneous system of equations.
Rank r =
Number of Variables n =
(b) Determine the rank of A.
(c) Use the results in parts (a) and (b) to determine the number of free variables (or parameters) in the general solution to the system of equations.
Number of Free Variables / =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643c9073-bfc9-41d3-b50c-3b14187fea75%2Ffded6f61-4660-4267-bebc-1ea5614cf7d2%2Figcseys_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the homogeneous system of equations with coefficient matrix
A =
9 2-1
0 1 -2
18 4 -4
[Recall: A homogeneous system is one where the right hand side of each equation is 0.]
(a) State the number of unknown variables in the homogeneous system of equations.
Rank r =
Number of Variables n =
(b) Determine the rank of A.
(c) Use the results in parts (a) and (b) to determine the number of free variables (or parameters) in the general solution to the system of equations.
Number of Free Variables / =
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