I am a little confused about dimensions, if the nullspace of a matrix is spanned by the 0 vector, does that mean the dimension of the nullspace of this matrix is 0?(adsbygoogle = window.adsbygoogle || []).push({});

In the problems I attached, both A and B reduced to the identity matrix.

Note (2) is supposed to be dim(N(B)) and dim(col(B)) instead of dim(N(A)) and dim(col(A)).

Since they both reduce to I, that means a pivot is in every column, which means that the dimension of N(A) and N(B) is 0 right?

Consequently, this means dim(Col(A)) and dim(col(B)) is 3 right?

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# Homework Help: Confused about dimensions

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