djeljenike

2021-09-13

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

$A=\left[\begin{array}{ccccc}1& 2& -5& 11& -3\\ 2& 4& -5& 15& 2\\ 1& 2& 0& 4& 5\\ 3& 6& -5& 19& -2\end{array}\right]$

$B=\left[\begin{array}{ccccc}1& 2& 0& 4& 5\\ 0& 0& 5& -7& 8\\ 0& 0& 0& 0& -9\\ 0& 0& 0& 0& 0\end{array}\right]$

BleabyinfibiaG

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:

to get:

And a basis for Nul A is

Result: Basis for Col A is:

Basis for Nul A is

An object moving in the xy-plane is acted on by a conservative force described by the potential energy function

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?

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