Find the Rank [[1,-1,3],[6,7,-3],[9,4,6]]

Problem

rank(1)

Solution

1. Set up the matrix A for row reduction to find the number of linearly independent rows.

A=[[1,−1,3],[6,7,−3],[9,4,6]]

2. Eliminate the first entry of the second and third rows by performing row operations (R_2)→(R_2)−6*(R_1) and (R_3)→(R_3)−9*(R_1)

[[1,−1,3],[0,13,−21],[0,13,−21]]

3. Eliminate the second entry of the third row by performing the row operation (R_3)→(R_3)−(R_2)

[[1,−1,3],[0,13,−21],[0,0,0]]

4. Identify the number of non-zero rows in the row echelon form, which represents the rank of the matrix.

rank(A)=2

Final Answer

rank(1)=2

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