Find Reduced Row Echelon Form [[-1,5],[0,0]]

Problem

[[−1,5],[0,0]]

Solution

1. Identify the first non-zero entry in the first row, which is −1 This will be the location of our first pivot.

2. Normalize the first row by multiplying it by −1 to make the leading coefficient equal to 1

−1⋅[[−1,5]]=[[1,−5]]

3. Check the remaining rows. The second row is already all zeros, so no further row operations are required to create zeros below the pivot.

4. Verify that the matrix satisfies the conditions for Reduced Row Echelon Form: the first non-zero entry in each row is 1 and it is the only non-zero entry in its column.

Final Answer

rref*([−1,5],[0,0])=[[1,−5],[0,0]]

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