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The matrix is singular because the last equation is the same as the second equation (simply multiplying every term in an equation by the same number (in this case, 2) does not produce an equation with new information).

for example

1) 3x=3y

2) 2x=2y

has no useful solution beyond the information from 1) that x=y

You would get a singular matrix for this.

The Gauss-Jordan method will not solve equations which cannot be solved by the old "elimination method".

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Q: Solve system of equation using Gauss Jordan form- When I try to solve these I find that the matrix is singular. Does that mean no solution x plus 2y-3z equals 1 y-2z equals 2 2y-4z equals 4?
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