Find Reduced Row Echelon Form [[1.61804,1],[1,0.61804]]

Problem

[[1.61804,1],[1,0.61804]]

Solution

1. Swap rows to place a 1 in the first pivot position.

[[1,0.61804],[1.61804,1]]

2. Eliminate the entry below the first pivot by performing the row operation (R_2)→(R_2)−1.61804*(R_1)

1−(1.61804)*(0.61804)≈1−1.0000055416

[[1,0.61804],[0,−0.0000055416]]

3. Identify that the value −0.0000055416 is a result of rounding the golden ratio ϕ≈1.61803398... where ϕ−1=1/ϕ Since (1.61804)*(0.61804)≈1 the second row is effectively a multiple of the first, making the determinant zero.

[[1,0.61804],[0,0]]

Final Answer

rref*[[1.61804,1],[1,0.61804]]=[[1,0.61804],[0,0]]

Want more problems? Check here!