Find Reduced Row Echelon Form [[0.8,-0.6],[0.6,0.8]]

Problem

[[0.8,−0.6],[0.6,0.8]]

Solution

1. Multiply the first row by 10 and the second row by 10 to eliminate decimals.

[[8,−6],[6,8]]

2. Divide the first row by 2 and the second row by 2 to simplify the integers.

[[4,−3],[3,4]]

3. Normalize the first row by multiplying (R_1) by 1/4 to create a leading 1

[[1,−0.75],[3,4]]

4. Eliminate the first entry of the second row by performing (R_2)−3*(R_1)⇒(R_2)

[[1,−0.75],[0,6.25]]

5. Normalize the second row by multiplying (R_2) by 1/6.25 (which is 0.16 to create a leading 1

[[1,−0.75],[0,1]]

6. Eliminate the second entry of the first row by performing (R_1)+0.75*(R_2)⇒(R_1)

[[1,0],[0,1]]

Final Answer

rref*([0.8,−0.6],[0.6,0.8])=[[1,0],[0,1]]

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