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What is the dimension of the subspace of solutions to the homogeneous system $Ax = 0$ called?

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Nullity

The nullity of a matrix is the number of free variables in its reduced row echelon form. According to the Rank-Nullity Theorem, the rank plus the nullity equals the number of columns in the matrix.

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  • What term describes the number of free variables in the reduced row echelon form of a matrix?

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