Assume that A is row equivalent to B. Find bases for Nul A and Col A.



Answered question


Suppose that A is row equivalent to B. Find bases for the null space of A and the column space of A.

Answer & Explanation



Skilled2021-09-14Added 118 answers

Since B is a row echelon form of A, we see that the first, third and fifth columns of A are its pivot columns. Thus a basis fo Col A is
To find a basis for Nul A, we find the general solution of Ax=0 in terms of the free variables. Since it is row equivalent to B we can simply get reduced row echelon form of B:
[12045005780000900000]R215R2R319R3  [120450057500000100000]
to get: x1=2x24x4,x3=75x4, x5=0, with x2 and x4 free. So
And a basis for Nul A is
Result: Basis for Col A is:
Basis for Nul A is

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?