![]() ![]() This quantity is called the rank of A A A, and denoted rk ( A ) \text. If R ( A ) R(A) R ( A ) denotes the row space of A A A and C ( A ) C(A) C ( A ) denotes the column space of A A A, then dim ( R ( A ) ) = dim ( C ( A ) ) \dim\big(R(A)\big) = \dim\big(C(A)\big) dim ( R ( A ) ) = dim ( C ( A ) ). ![]() It is an important fact that the row space and column space of a matrix have equal dimensions. The simplest way to find it is to reduce the matrix to its simplest form. Use this free online algebra calculator to find the rank of a matrix of 3x3 dimension. In linear algebra, the rank of a matrix is the dimension of its row space or column space. In linear algebra, Matrix rank is the maximum number of independent row or column vectors in the matrix. ![]()
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