Question
In Exercises \( 29-36 \), state the next elementary row operation that should be performed in order to put the matrix into diagonal form. Do not perform the operation. 29. \( \left[\begin{array}{rr|r}1 & -5 & 1 \\ -2 & 4 & 6\end{array}\right] \)
Ask by Grant Delgado. in the United States
Feb 25,2025
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Answer
To eliminate the -2 in the second row, add 2 times the first row to the second row.
Solution
To put the matrix
\[
\left[\begin{array}{rr|r}1 & -5 & 1 \\ -2 & 4 & 6\end{array}\right]
\]
into diagonal form, we need to eliminate the entry below the leading 1 in the first column.
The current leading entry is in the first row and first column (which is 1). The entry below it in the second row and first column is -2.
To eliminate this -2, we can perform the following elementary row operation:
**Add 2 times the first row to the second row.**
This operation will change the second row to eliminate the -2, moving us closer to diagonal form.
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Simplify this solution Bonus Knowledge
To begin placing the matrix into diagonal form, you'll want to eliminate the leading coefficient in the second row. So, the next elementary row operation should be to add 2 times the first row to the second row. This will help create a zero beneath the leading 1 in the first column, setting you up for a diagonal approach. Following that, keep in mind that after this operation, it's crucial to make sure that any entries in rows below the pivot row (the first row in this case) are systematically eliminated, leading towards a neat diagonal arrangement. Just be cautious of keeping track of the coefficients as you make each operation!
