Find the Rank [[3,3],[3,3]]

Problem

rank(3)

Solution

1. Identify the matrix A as a 2×2 matrix where all entries are equal.

A=([3,3],[3,3])

2. Perform row reduction by subtracting the first row from the second row to create a row of zeros.

(R_2)→(R_2)−(R_1)

([3,3],[0,0])

3. Normalize the first row by dividing by 3 to reach row-echelon form.

(R_1)→1/3*(R_1)

([1,1],[0,0])

4. Determine the rank by counting the number of non-zero rows in the row-echelon form.

rank(A)=1

Final Answer

rank(3)=1

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