Null, column and row space

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In mathematics a matrix can be categorised by its null, column and to a lesser extent its column space. These are all vector spaces associated with a particular matrix.

Null space

The null space of a matrix is as,

.

The null space is all so known as the solution space.

Column space

The column space is the vector space formed by the span of the columns of the matrix .

Row Space

The rows space is the vector space formed by the span of the rows of the matrix .