Find Reduced Row Echelon Form [[-3,6,21,30],[1,4,9,12]]

Problem

[[−3,6,21,30],[1,4,9,12]]

Solution

1. Write the augmented matrix representing the system.

[[−3,6,21,30],[1,4,9,12]]

2. Swap the first and second rows to obtain a leading 1 in the first row.

(R_1)↔(R_2)

[[1,4,9,12],[−3,6,21,30]]

3. Eliminate the first entry in the second row by adding 3 times the first row to the second row.

(R_2)+3*(R_1)⇒(R_2)

[[1,4,9,12],[0,18,48,66]]

4. Divide the second row by 18 to create a leading 1 in the second row.

1/18*(R_2)⇒(R_2)

[[1,4,9,12],[0,1,8/3,11/3]]

5. Eliminate the entry above the leading 1 in the second column by subtracting 4 times the second row from the first row.

(R_1)−4*(R_2)⇒(R_1)

[[1,0,9−32/3,12−44/3]]

[[1,0,−5/3,−8/3],[0,1,8/3,11/3]]

Final Answer

rref*([−3,6,21,30],[1,4,9,12])=[[1,0,−5/3,−8/3],[0,1,8/3,11/3]]

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