 # The reduced row echelon form of the augmented matrix of a system of three linear equations in 3 variables must be of the form where a,b,c are real nmb remolatg 2021-09-11 Answered

The reduced row echelon form of the augmented matrix of a system of three linear equations in three variables must be of the form $$\begin{bmatrix}1&0&0 \\0&1&0 \\0&0&1\\a&b&c \end{bmatrix}$$ where a, b, c, are real numbers. Justify your answer.

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Reduced row echelon form consists of the first row starting off with a 1 followed by 0's until the last column which contains a real number, the second row starts off with a 0 in the first column and a 1 in the second column followed by 0's until the last column, this continues on depending on the number of rows and columns.
In the problem it is set up this way replacing the last column with variables which stand for a real number which makes the equation true.