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## Main Question or Discussion Point

Why is the row space of a matrix important?

- Thread starter matqkks
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Why is the row space of a matrix important?

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One example is basic multiplication;

Multiplying a matrix with a vector to the right gives linear combinations of the columns, multiplying with a vector to the left gives linear combinations of the rows.

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Bacle2

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The row space is used in the fundamental theorem of linear algebra:

http://en.wikipedia.org/wiki/Fundamental_theorem_of_linear_algebra

which relates row space, column space, kernel and cokernel.

Together, of course, with the rank-nullity theorem.

http://en.wikipedia.org/wiki/Fundamental_theorem_of_linear_algebra

which relates row space, column space, kernel and cokernel.

Together, of course, with the rank-nullity theorem.

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