Rank Calculation for Null Matrix
A null matrix, often denoted as $O$ or $A$ in this context, is a matrix where all its entries are zero.
The rank of a matrix is defined as the maximum number of linearly independent row vectors (or column vectors) in the matrix. It also corresponds to the dimension of the row space or column space.
Determining Rank of Zero Matrix
- For a null matrix $A$, every row is a zero vector. For example, if $A$ is $3 \times 3$, it looks like: $ A = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} $
- The zero vector is considered linearly dependent. Since all rows (or columns) are zero vectors, there are no linearly independent rows (or columns) that form a basis for a non-zero dimensional vector space.
- The dimension of the vector space spanned by the zero vector(s) is 0.
- Therefore, the rank of any null matrix $A$ is 0.
This matches Option 2.
Important Questions from Mixed Topic (CUET PG)
- Who was the founder of Bolshevik Communist party?
- What is the key guide to statecraft in the realist tradition?
- Chronologically arrange the events in the Cold War period.
A. Berlin Wall is constructed
B. Communist China joins the UN
C. Soviet invasion of Czechoslovakia
D. Berlin Blockade
Choose the correct answer from the options given below: Morgenthau's principles of political realism are:
A. Politics is rooted in permanent and unchanging human nature which is basically self centred, self-regarding and self-interested
B. Politics is an autonomous sphere of action and cannot therefore be reduced to morals
C. International Politics is an arena of conflicting self-interests
D. The ethics of international relations is situational ethics which is very different from private morality
Choose the correct answer from the options given below:Who among the following political thinkers consider the anarchical self help system to be a compelling factor for States to maximise their relative power positions?
