What is Rank of Matrices-

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Standard XI

Mathematics

Rank of a Matrix

What is Rank ...

Question

What is the rank of matrices?

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Solution

Rank of matrices:
The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix.
The rank of a matrix cannot exceed the number of its rows or columns.
Minor method and Echelon form are two popular methods to find the rank of matrices.

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Q. Find the rank of the following matrices:

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 5 & 9 4 & 8 & 12 7 & 11 & 15 \end{matrix} ⎤ ⎥ ⎦

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Q. Arrange the given matrices in ascending order of their ranks.

⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & - 1 2 & 3 & 0 0 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦

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What is the rank of matrices?

Rank of matrices:The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix.The rank of a matrix cannot exceed the number of its rows or columns.Minor method and Echelon form are two popular methods to find the rank of matrices.

Rank of matrices:
The maximum number of its linearly independent columns (or rows ) of a matrix is called the rank of a matrix.
The rank of a matrix cannot exceed the number of its rows or columns.
Minor method and Echelon form are two popular methods to find the rank of matrices.