Find the Rank

Problem

rank(1)

Solution

1. Set up the matrix A for row reduction.

A=[[1,2,3,4],[2,1,4,5],[1,5,5,7],[8,1,14,17]]

2. Eliminate the first column entries below the first row using row operations (R_2)→(R_2)−2*(R_1) (R_3)→(R_3)−(R_1) and (R_4)→(R_4)−8*(R_1)

[[1,2,3,4],[0,−3,−2,−3],[0,3,2,3],[0,−15,−10,−15]]

3. Eliminate the second column entries below the second row using row operations (R_3)→(R_3)+(R_2) and (R_4)→(R_4)−5*(R_2)

[[1,2,3,4],[0,−3,−2,−3],[0,0,0,0],[0,0,0,0]]

4. Identify the number of non-zero rows in the row echelon form.

Number of non-zero rows=2

Final Answer

rank(1)=2

Want more problems? Check here!