Question
If A is a null Matrix, then its rank is :
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CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
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Null Matrix Rank Explained
A null matrix, often called a zero matrix, is a matrix where every element is zero.
Example:
$ A = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} $
Understanding Matrix Rank
The rank of a matrix is the dimension of the vector space formed by its columns (or rows). It signifies the maximum number of linearly independent columns or rows within the matrix.
Rank of the Null Matrix
For a null matrix:
- All its rows (and columns) are zero vectors.
- The vector space spanned by these zero vectors contains only the zero vector, denoted as {0}.
- The dimension of a space containing only the zero vector is 0.
Consequently, the $rank$ of any null matrix is always 0.
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