Question

What is the rank of $3\times 3$ a matrix?

Answer 1

Rank of matrix:

A rectangular set of numbers displayed in the form of rows and columns is a matrix. A matrix is denoted as ${\mathrm{a}}_{\mathrm{i}\times \mathrm{j}}$, where $\mathrm{i}$ is the number of rows and $\mathrm{j}$ is the number of columns.

The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix.

Rank of $3\times 3$ matrix:

In a $3\times 3$ matrix, there are $3$ rows and $3$columns. The rank of the $3\times 3$ matrix can be either $3$or less than $3$.

Hence, the rank of the $3\times 3$matrix is less than or equal to $3$.