Determine which matrices are in reduced echelon form and which others are only in echelon form. a)begin{bmatrix}1&0&1&0 0&1&1&00&0&0&1 end{bmatrix} b)begin{bmatrix}0&1&1&1&1 0&0&1&1&10&0&0&0&10&0&0&0&0 end{bmatrix} c)begin{bmatrix}1&5&0&0 0&0&1&00&0&0&00&0&0&1 end{bmatrix}

Determine which matrices are in reduced echelon form and which others are only in echelon form.
a)$\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 1& 0\\ 0& 0& 0& 1\end{array}\right]$
b)$\left[\begin{array}{ccccc}0& 1& 1& 1& 1\\ 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\end{array}\right]$
c)$\left[\begin{array}{cccc}1& 5& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\end{array}\right]$ ф
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Step 1
To Determine which matrices are in reduced echelon form and which others are only in echelon form.
Step 2
Given that
a)$\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 1& 0\\ 0& 0& 0& 1\end{array}\right]$
According to the definition we conclude that matrix is in reduced row echeclon form because the leading entry in each nonzero row is 1 and each leading 1 is the only nonzero entry in its column.

Given that
b)$\left[\begin{array}{ccccc}0& 1& 1& 1& 1\\ 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0\end{array}\right]$
According to the definition the matrix is in echelon form only.
Echelon form only.
c)Given that
$\left[\begin{array}{cccc}1& 5& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\end{array}\right]$
According to the definition we conclude that matrix is not in echelon form and that matrix not in reduced row echelon form.
Jeffrey Jordon