Determine by inspection (i.e., without performing any calculations) whether a linear system with the given augmented matrix has a unique solution, infinitely many solutions, or no solution 3-2 0 1 1 1 2 -3 1 2 4 -6 2 O unique solution O infinitely many solutions O no solution 0 Justify your answer. O The matrix can be rewritten in row echelon form with no free variables. O The matrix can be rewritten in row echelon form with two free variables. O The matrix can be rewritten in row echelon form with one free variable. O The matrix can be rewritten so that you have a row 0 0 0 0 | a with a = 0. O This system is a homogeneous system with four variables and only three equations, so the rank of the matrix is at most 3 and thus there is at least one free variable.
Determine by inspection (i.e., without performing any calculations) whether a linear system with the given augmented matrix has a unique solution, infinitely many solutions, or no solution 3-2 0 1 1 1 2 -3 1 2 4 -6 2 O unique solution O infinitely many solutions O no solution 0 Justify your answer. O The matrix can be rewritten in row echelon form with no free variables. O The matrix can be rewritten in row echelon form with two free variables. O The matrix can be rewritten in row echelon form with one free variable. O The matrix can be rewritten so that you have a row 0 0 0 0 | a with a = 0. O This system is a homogeneous system with four variables and only three equations, so the rank of the matrix is at most 3 and thus there is at least one free variable.
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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Transcribed Image Text:Determine by inspection (i.e., without performing any calculations) whether a linear system with the given augmented matrix has a unique solution, infinitely many solutions, or no solution.
3-2 0 1 1
1 2 -3 1
2 4 -6 2
O unique solution
O infinitely many solutions
O no solution
0
Justify your answer.
O The matrix can be rewritten in row echelon form with no free variables.
O The matrix can be rewritten in row echelon form with two free variables.
O The matrix can be rewritten in row echelon form with one free variable.
O The matrix can be rewritten so that you have a row 0 0 0 0 | a with a = 0.
O This system is a homogeneous system with four variables and only three equations, so the rank of the matrix is at most 3 and thus there is at least one free variable.
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