Chapter 7.1, Problem 100E

(a)

To determine

Whether the matrix $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ is in row echelon form, reduced echelon form, or neither, if it satisfies the condition $b=0,c=0$.

(b)

To determine

Whether the matrix $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ is in row echelon form, reduced echelon form, or neither, if it satisfies the condition $b\ne 0,c=0$.

(c)

To determine

Whether the matrix $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ is in row echelon form, reduced echelon form, or neither, if it satisfies the condition $b=0,c\ne 0$.

(d)

To determine

Whether the matrix $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ is in row echelon form, reduced echelon form, or neither, if it satisfies the condition $b\ne 0,c\ne 0$.