Courses   <-  Sean Forman   <-  You Are Here Reduced Row-Echelon Form

MAT 1151, Business Math, Sean Forman

None of the following matrices are in RRE form. State which rule(s) prevent this matrix from being in RRE form. Then perform an operation that will make the matrix in RRE form.

Rules (p. 200)

1. All zeros rows must be below all non-zero rows.

2. The first non-zero element of every non-zero row is a one (these are ``leftmost ones'')

3. The column of each leftmost one contains only zeros in the other rows.

4. Each leftmost one appears to the right of any leftmost ones in the rows above it.

1. $\left( \begin{array}{r r r r} 1 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 3 \end{array}\right)$
   
   
   
   
   
   

2. $\left( \begin{array}{r r r r} 1 & 1 & 0 & 4 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 1 \end{array}\right)$
   
   
   
   
   
   

3. $\left( \begin{array}{r r r r} 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 1 & 0 & 4 \end{array}\right)$
   
   
   
   
   
   

4. $\left( \begin{array}{r r r r} 1 & 1 & 0 & 4 \\ 0 & 0 & 3 & 6 \\ 0 & 0 & 0 & 0 \end{array}\right)$
   
   
   
   
   
   

5. $\left( \begin{array}{r r r r} 1 & -1 & 0 & 2 \\ 0 & 1 & 2 & 4 \\ 0 & 0 & 1 & 1 \end{array}\right)$
   
   
   
   
   
   

6. $\left( \begin{array}{r r r r} 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 6 \\ 0 & 1 & 2 & -5 \end{array}\right)$
   
   
   
   
   
   

7. $\left( \begin{array}{r r r r} 2 & 0 & 0 & 0 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)$
   
   
   
   
   
   

8. $\left( \begin{array}{r r r r} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 \end{array}\right)$