Reduced Row Echelon Form and Row Operations

Practice Questions

Linear Algebra › Reduced Row Echelon Form and Row Operations

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Find the inverse using row operations

$\begin{bmatrix} 2 &7 &1 \-1 &5 &3 \ 2& 2& -1\end{bmatrix}$

$\begin{align*}&\text{Convert }A=\begin{bmatrix}4&-9&-10\-11&-13&-5\\end{bmatrix}\&\text{to its reduced echelon form.}\end{align*}$

$\begin{align*}&\text{Find the reduced echelon form of the matrix:}\&\begin{bmatrix}-1&11&-19\-13&-17&4\\end{bmatrix}\end{align*}$

$A = \begin{bmatrix}\bigcirc & \bigcirc & \bigcirc & \bigcirc \ 0 & 1 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix}$

Note that the top row is missing. How many ways can the top row be completed in order to form a matrix in reduced row-echelon form?

True or false:

$\begin{bmatrix}1 &0 &0&0 \0 &1 &0&0 \ 0 &0 &1 &0 \1,000,000 &0&0&1\end{bmatrix}$

is an elementary matrix.

True or false:

$\begin{bmatrix} 0.000001 &0 &0&0 \0 &1 &0&0 \ 0 &0 &1 &0 \0 &0&0&1\end{bmatrix}$

is an elementary matrix.

True or false:

$\begin{bmatrix}1 &0 &0&0 \0 &1 &0&0 \ 0 &0 &1 &0 \1 & 1& 1&1\end{bmatrix}$

is an elementary matrix.

Is the following matrix in reduced row echelon form? Why or why not.

$\begin{bmatrix} 5& 0& 0& 7\ 0& 1& 0& 5\ 0& 0& 1& 4 \end{bmatrix}$

$A= \begin{bmatrix} 0 & 1 & 0 & 1 \ 1 & 0 & 0 & 2 \ 0 & 0 & 1 & -3 \end{bmatrix}$

True or false: is an example of a matrix in reduced row-echelon form.

$A= \begin{bmatrix} 1 & 0 & 1 & 0 \ 0 & 1 & -2 & 0 \ \bigcirc &\bigcirc &\bigcirc &\bigcirc \end{bmatrix}$ .

Note that the entries in the bottom row are missing.

How many possible ways can the entries in the bottom row be filled in so that is in reduced row-echelon form?

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