Chapter 1, Problem 74RE

(a)

To determine

To describe: The reduced row echelon form of the augmented matrix $\left[\begin{array}{cc}A& 0\end{array}\right]$ where A is an $m\times n$ matrix with reduced row echelon matrix R and 0 is the $m\times 1$ zero vector.

(b)

To determine

To describe: The reduced row echelon form of the matrix $\left[\begin{array}{cccc}{\text{a}}_1& {\text{a}}_2& \cdots & {\text{a}}_k\end{array}\right]$ for $k<n$ where ${\text{a}}_i$ denotes the ith column of the $m\times n$ matrix A.

(c)

To determine

To describe: The reduced row echelon form of the matrix cA where A is an $m\times n$ matrix with reduced row echelon matrix R and c is a nonzero scalar.

(d)

To determine

To describe: The reduced row echelon form of the augmented matrix $\left[\begin{array}{cc}{I}_m& A\end{array}\right]$ where A is an $m\times n$ matrix and $I_m$ is the $m\times m$ identity matrix.

(e)

To determine

To describe: The reduced row echelon form of the augmented matrix $\left[\begin{array}{cc}A& cA\end{array}\right]$ where A is an $m\times n$ matrix with reduced row echelon matrix R and c is any scalar.