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how do i tell if a matrix is reduced?
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As in reduced to row-echelon form? Are the leading coefficients all 1 and does it follow an upside-down stair pattern?
yes, row echelon form
\[\left[\begin{matrix}1 & a &b \\ 0 & 1 &c \\ 0 & 0 & 1 \end{matrix}\right]\] This is an example of row-echelon form for a 3x3 matrix. You just need to see if it has the 1s in the diagonal and the upside-down stair pattern.
The conclusion you can give out is the solution of the system from r.r.e.f. You can say whether the system has solution or not and how many of them.
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