Find the Rank [[10,20,30,40]]

Problem

rank(10)

Solution

1. Identify the dimensions of the given matrix. The matrix is a row vector with 1 row and 4 columns, making it a 1×4 matrix.

2. Determine the maximum possible rank. The rank of a matrix is at most the minimum of its number of rows and columns, so rank(A)≤min(1,4)=1

3. Check for non-zero elements. Since the matrix contains at least one non-zero entry (in fact, all entries are non-zero), the row is linearly independent.

4. Conclude the rank. A non-zero row vector always has a rank of 1.

Final Answer

rank(10)=1

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