Chapter 8.1, Problem 100E

a.

To determine

To find:Whether the given matrix is in row-echelon form, reduced row-echelon form, or neither when it satisfies the given condition.

Answer to Problem 100E

The matrix is in reduced row-echelon form when the matrix satisfies the given condition.

Explanation of Solution

Given information:

The matrix is $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ and the condition is $b=0,c=0.$ .

When $b=0\text{and}c=0,$ the given matrix becomes

  $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ .

Conclusion:

Thus, it is in reduced row-echelon form.

b.

To determine

To find: Whether the given matrix is in row-echelon form, reduced row-echelon form, or neither when it satisfies the given condition.

Answer to Problem 100E

The matrix is in row-echelon form when the matrix satisfies the given condition.

Explanation of Solution

Given information:

The matrix is $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ and the condition is $b\ne 0,c=0$ .

When $b\ne 0\text{and}c=0$ , the given matrix becomes

  $\left[\begin{array}{cc}1& b\\ 0& 1\end{array}\right]$ .

Conclusion:

Thus, it is in row-echelon form.

c.

To determine

To find: Whether the given matrix is in row-echelon form, reduced row-echelon form, or neither when it satisfies the given condition.

Answer to Problem 100E

The matrix is in neither row-echelon form nor reduced row-echelon form when the matrix satisfies the given condition.

Explanation of Solution

Given information:

The matrix is $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ and the condition is $b=0,c\ne 0$ .

When $b=0\text{and}c\ne 0$ , the given matrix becomes

  $\left[\begin{array}{cc}1& 0\\ c& 1\end{array}\right]$ .

Conclusion:

Thus, it is in neither row-echelon form nor reduced row-echelon form.

d.

To determine

To find: Whether the given matrix is in row-echelon form, reduced row-echelon form, or neither when it satisfies the given condition.

Answer to Problem 100E

The matrix is in neither row-echelon form nor reduced row-echelon form when the matrix satisfies the given condition.

Explanation of Solution

Given information:

The matrix is $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ and the condition is $b\ne 0,c\ne 0$ .

When $b\ne 0\text{and}c\ne 0$ , the given matrix becomes

  $\left[\begin{array}{cc}1& b\\ c& 1\end{array}\right]$ .

Conclusion:

Thus, it is in neither row-echelon form nor reduced row-echelon form.