Find the Rank [[5,9,3],[3,5,6],[1,5,3]]

Problem

Rank*[[5,9,3],[3,5,6],[1,5,3]]

Solution

1. Set up the matrix A and prepare for row reduction to find the number of non-zero rows in row-echelon form.

A=[[5,9,3],[3,5,6],[1,5,3]]

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

(R_1)↔(R_3)⇒[[1,5,3],[3,5,6],[5,9,3]]

3. Eliminate the first entries of the second and third rows using the first row.

(R_2)−3*(R_1)→(R_2)⇒[[1,5,3],[0,−10,−3],[5,9,3]]

(R_3)−5*(R_1)→(R_3)⇒[[1,5,3],[0,−10,−3],[0,−16,−12]]

4. Simplify the second row by dividing by −10 to create a leading 1

−1/10*(R_2)→(R_2)⇒[[1,5,3],[0,1,0.3],[0,−16,−12]]

5. Eliminate the second entry of the third row using the second row.

(R_3)+16*(R_2)→(R_3)⇒[[1,5,3],[0,1,0.3],[0,0,−7.2]]

6. Identify the number of non-zero rows. Since there are three rows with non-zero entries, the matrix is of full rank.

Final Answer

Rank*[[5,9,3],[3,5,6],[1,5,3]]=3

Want more problems? Check here!