Suppose that A is row equivalent to B. Find bases for the null space of A and the column space of A.
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:
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
I need to find a unique description of Nul A, namely by listing the vectors that measure the null space
T must be a linear transformation, we assume. Can u find the T standard matrix.?
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7).
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R.
b) Find the area of the triangle PQR.
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