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+6 votes
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Consider the following system of equations:  

$3x + 2y = 1 $

$4x + 7z = 1 $

$x + y + z = 3$

$x - 2y + 7z = 0$

The number of solutions for this system is ______________
asked in Linear Algebra by Veteran (87.2k points)   | 1.1k views

4 Answers

+11 votes
Best answer
Since equation (2) - equation (1) produces equation (4), we have 3 independent equations in 3 variables, hence unique solution.

So answer is 1.
answered by Veteran (10.9k points)  
selected
+5 votes

sorry for my handwriting!

answered by Active (2k points)  
+2 votes
Can someone plz find the rank of thie matrix using row transformations.I m not able to do so.Plz help
answered by Active (1.2k points)  
rank(A) = rank(AB) = n (no. of unknowns) =3
Even i am getting rank as 4 although its not possible.
Rank will be 4 if you solve all 4 equations together. But note that 2 rows in Echelon form will be identical.
0 votes
rank(Augmented Matrix) = rank(Matrix) = no of unknowns. Hence it has a unique solution
answered by Loyal (4k points)  


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