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A matrix in reduced row echelon form is used to solve systems of linear equations. There are four prerequisites for the reduced row echelon form:

• The number 1 is the first non-zero integer in the first row (the leading entry).
• The second row begins with the number 1, which is more to the right than the first row's leading item. The number 1 must be further to the right in each consecutive row.
• Each row's first item must be the sole non-zero number in its column.
• Any rows that are not zero are pushed to the bottom of the matrix.

A is a 4 脳 3 matrix, and $\stackrel{鈫�}{b}$and$\stackrel{鈫�}{c}$ are two vectors in ${\mathrm{鈩�}}^4$and the system $A\stackrel{鈫�}{x}=\stackrel{鈫�}{b}$has a unique solution.

As the system $A\stackrel{鈫�}{x}=\stackrel{鈫�}{b}$has unique solution, thus, the reduced row-echelon form of the matrix A will be,

$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 0& 0& 0\end{array}\right]$

Thus, if $A\stackrel{鈫�}{x}=\stackrel{鈫�}{b}$has a unique solution, then $A\stackrel{鈫�}{x}=\stackrel{鈫�}{c}$will have unique solution.

As the system $A\stackrel{鈫�}{x}=\stackrel{鈫�}{b}$has unique solution, thus, the system role="math" localid="1659342182678" $A\stackrel{鈫�}{x}=\stackrel{鈫�}{c}$will have unique solution.