Simple Q about calculating Nullspace

Thread starter 11markus04
Start date Jan 11, 2011
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Nullspace

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When calculating the nullspace of an n x n matrix, it is not necessary for all pivots to be 1 after reducing the matrix to row echelon form. The presence of zero pivots does not affect the ability to identify free variables or compute the vectors that satisfy Ax=0. Having pivots equal to 1 simplifies the arithmetic but is not a requirement for the calculation. The focus should be on the row echelon form rather than the specific values of the pivots. Understanding this allows for flexibility in determining the nullspace.

Jan 11, 2011

11markus04

When calculating the nullspace of a n x n matrix, after i have reduced the matrix to row echelon form, DO ALL MY PIVOTS HAVE TO BE 1 BEFORE i can distinguish the free variables, and then calculate the vectors that satisfy Ax=0?

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Jan 12, 2011

HallsofIvy

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No, it really doesn't matter if the pivots are 0. That just makes the arithmetic easier since if they are you don't have to divide.

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