Find Reduced Row Echelon Form [[2n],[n-1]]

Problem

[[2*n],[n−1]]

Solution

1. Identify the matrix as a 2×1 column vector.

2. Divide the first row by 2*n to create a leading 1 in the first entry, assuming n≠0

(R_1)→1/(2*n)*(R_1)

[[1],[n−1]]

3. Eliminate the entry in the second row by subtracting (n−1) times the first row from the second row.

(R_2)→(R_2)−(n−1)*(R_1)

[[1],[(n−1)−(n−1)*(1)]]

4. Simplify the second row entry to zero.

[[1],[0]]

Final Answer

rref*([2*n],[n−1])=[[1],[0]]

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