ediculeN

2021-01-13

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)$\left[\begin{array}{cccc}1& 5& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 1\end{array}\right]$

hosentak

Skilled2021-01-14Added 100 answers

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.

$\therefore \text{Reduced row echelon form}$

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.

Answer: Neither

To Determine which matrices are in reduced echelon form and which others are only in echelon form.

Step 2

Given that

a)

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)

According to the definition the matrix is in echelon form only.

Echelon form only.

c)Given that

According to the definition we conclude that matrix is not in echelon form and that matrix not in reduced row echelon form.

Answer: Neither

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Answer is given below (on video)

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