Question

The number of pivot columns of a matrix equals the dimension of its column space. (T/F)

Answer 1

The number of pivot columns of a matrix equals the dimension of its column space is true statement.

As given in the question,

The number of pivot columns of a matrix equals the dimension of its column space is true statement as per following reasons

• The pivot columns of any
• matrix
• are linearly independent.
• The pivot columns span the column space to form a basis of column space in the given
• matrix
• .

Therefore, the number of pivot columns of a matrix equals the dimension of its column space.

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