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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 ______________

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

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I could not understand this.. Can u please elaborate more
And solution is x=13,y=-19,z=9 only single solution
Finding rank of 4x4 matrix is quite time consuming .But logic should be clear.

Which three equation are used to determine the answers is not mentioned.

sorry for my handwriting!

how did you make R4 all zeros?
if R4 is all zeros , then there is 3x3 square  matrix inside  the augmented matrix , for which the determinant is zero .. hence rank of the augmented matrix cannot be 3.
@shaurya

rank of augmented matrix(AB) >= rank of A.

In the pic R= R4 - R2 ..... And To be unique solution R(A|B) = R(A) =  n where n is # of variables ...

Can someone plz find the rank of thie matrix using row transformations.I m not able to do so.Plz help
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.
rank(Augmented Matrix) = rank(Matrix) = no of unknowns. Hence it has a unique solution