Find Reduced Row Echelon Form ([[-4,0],[8,1],[-4,-2]]*1)/2

Problem

1/2*[[−4,0],[8,1],[−4,−2]]

Solution

1. Multiply the matrix by the scalar 1/2 to simplify the entries.

[[−2,0],[4,0.5],[−2,−1]]

2. Normalize the first row by dividing by −2 to create a leading 1 in the first column.

[[1,0],[4,0.5],[−2,−1]]

3. Eliminate the entries below the leading 1 in the first column by performing row operations (R_2)−4*(R_1)⇒(R_2) and (R_3)+2*(R_1)⇒(R_3)

[[1,0],[0,0.5],[0,−1]]

4. Normalize the second row by multiplying by 2 to create a leading 1 in the second column.

[[1,0],[0,1],[0,−1]]

5. Eliminate the entry below the leading 1 in the second column by performing the row operation (R_3)+(R_2)⇒(R_3)

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

Final Answer

rref*(1/2*[[−4,0],[8,1],[−4,−2]])=[[1,0],[0,1],[0,0]]

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