User row operations to change the matrix to reduced form.
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Question

Quizplus · Accepted Answer

We can use row operations to change the matrix to reduced form. Specifically, we can perform the following steps: 
1. Subtract the first row from the second row 
2. Divide the second row by -5 
3. Subtract 5 times the second row from the third row 
4. Divide the third row by -3 
5. Add the third row to the first row 
The resulting matrix will be in reduced form and will be option C. Performing row operations, the matrix can be transformed to:
$$
\begin{bmatrix}
1 & 2 & 4 \
0 & 1 & 2 \
0 & 0 & 0 
\end{bmatrix}
$$
This is the reduced row echelon form because:
1. The leading entry of each non-zero row is 1.
2. The leading 1 of each row is to the right of the leading 1 of the row above it.
3. All entries in a column below a leading 1 are zero.
Option C is the only one that matches this reduced form.

User Row Operations to Change the Matrix to Reduced Form