Find Reduced Row Echelon Form [[1,4,15],[6,0,18]]

Problem

[[1,4,15],[6,0,18]]

Solution

1. Identify the first pivot in the first row, which is already 1 in the first column.

2. Eliminate the entry below the first pivot by performing the row operation (R_2)−6*(R_1)⇒(R_2)

(R_2)−6*(1,4,15)=(6−6,0−24,18−90)=(0,−24,−72)

[[1,4,15],[0,−24,−72]]

3. Normalize the second row to create a pivot of 1 by performing the row operation −1/24*(R_2)⇒(R_2)

−1/24*(0,−24,−72)=(0,1,3)

[[1,4,15],[0,1,3]]

4. Eliminate the entry above the second pivot by performing the row operation (R_1)−4*(R_2)⇒(R_1)

(R_1)−4*(0,1,3)=(1−0,4−4,15−12)=(1,0,3)

[[1,0,3],[0,1,3]]

Final Answer

rref*([1,4,15],[6,0,18])=[[1,0,3],[0,1,3]]

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