Simplify the Matrix

Problem

[[5,4,3,2],[1,2,3,4],[5,4,3,2],[1,2,3,4]]

Solution

1. Identify the structure of the matrix and notice that the first row is identical to the third row, and the second row is identical to the fourth row.

2. Perform row operations to simplify the matrix by subtracting the first row from the third row ((R_3)−(R_1)→(R_3) and subtracting the second row from the fourth row ((R_4)−(R_2)→(R_4).

3. Observe that these operations result in two rows of zeros, indicating that the matrix has a rank of 2.

4. Conclude that the simplified row echelon form (REF) or the reduced row echelon form (RREF) is the standard way to represent a simplified matrix.

Final Answer

[[5,4,3,2],[1,2,3,4],[5,4,3,2],[1,2,3,4]]=[[1,0,−1,−2],[0,1,2,3],[0,0,0,0],[0,0,0,0]]

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