Find the Rank

Problem

rank(1)

Solution

1. Identify the matrix A and observe its structure.

A=[[1,0,−4,0,−2,3],[0,1,7,−1,0,5],[0,0,0,0,1,0],[0,0,0,0,0,0]]

2. Check if the matrix is in row echelon form (REF). A matrix is in REF if all non-zero rows are above any rows of all zeros, and the leading coefficient of a non-zero row is always strictly to the right of the leading coefficient of the row above it.

3. Locate the pivots (the first non-zero entry in each non-zero row).

• In row 1, the pivot is 1 at column 1.

• In row 2, the pivot is 1 at column 2.

• In row 3, the pivot is 1 at column 5.

• Row 4 is a zero row and contains no pivots.

4. Determine the rank by counting the number of non-zero rows in the row echelon form. There are 3 non-zero rows.

Final Answer

rank(1)=3

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