- #1
charlies1902
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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?
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?
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?