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let a be an mn matrix. determine whether the statement below is true or false. justify the answer. the nullity of a is the number of columns of a that are not pivot columns.



Answer :

The given statement that the nullity of a is the number of columns of a that are not pivot columns is true.

what is know as nullity of a matrix?

  • A matrix's nullity is the dimension of A's null space, also known as the kernel of A. Null space (A) = 0 if A is an invertible matrix.
  • The rank of a matrix is the number of non-zero eigenvalues of the matrix, and the number of zero eigenvalues determines the nullity of the matrix.

Given that:

The nullity of A = [tex][a_{ij} ]_{m * n}[/tex] is the number of A that are not pivot columns.

The given statement is true.

Since the rank of A is equal to the no . of . columns which have pivot and nullity of A is equal to the no .of . columns which does not have pivot positions.

We know that ,

Rank A + nullity A = No . of . columns of A

To learn more about dimension check the given link

https://brainly.com/question/12968520

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