Find Reduced Row Echelon Form [[6,-4,10],[-1,0,6],[10,7,-4]]

Problem

[[6,−4,10],[−1,0,6],[10,7,−4]]

Solution

1. Swap the first and second rows to get a leading coefficient of −1 in the first row.

[[−1,0,6],[6,−4,10],[10,7,−4]]

2. Multiply the first row by −1 to create a leading 1

[[1,0,−6],[6,−4,10],[10,7,−4]]

3. Eliminate the first column entries below the leading 1 by performing (R_2)−6*(R_1)⇒(R_2) and (R_3)−10*(R_1)⇒(R_3)

[[1,0,−6],[0,−4,46],[0,7,56]]

4. Divide the second row by −4 to create a leading 1 in the second row.

[[1,0,−6],[0,1,−11.5],[0,7,56]]

5. Eliminate the second column entry below the leading 1 by performing (R_3)−7*(R_2)⇒(R_3)

[[1,0,−6],[0,1,−11.5],[0,0,136.5]]

6. Divide the third row by 136.5 to create a leading 1 in the third row.

[[1,0,−6],[0,1,−11.5],[0,0,1]]

7. Eliminate the third column entries above the leading 1 by performing (R_1)+6*(R_3)⇒(R_1) and (R_2)+11.5*(R_3)⇒(R_2)

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

Final Answer

rref*[[6,−4,10],[−1,0,6],[10,7,−4]]=[[1,0,0],[0,1,0],[0,0,1]]

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