Definitions:
1) The set of vectors
The map
(i)
(ii)
Let us consider an arbitrary representation of zero vector of V as a linear combination of vectors from S.
Since T is linear,
i.e.,
Thus,
By the linearity of T we have
since the set
substituting
Thus (1) will be the trivial representation of zero vector of V.
Hence
Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at
Suppose f is a differentiable function of x and y, and
g(r, s) = f(2r − s, s2 − 7r).
Use the table of values below to calculate
gr(4, 3)
and
gs(4, 3).
f  g  fx  fy  
(5, −19) 
4 
9 
7 
1 
(4, 3) 
9 
4 
5 
2 
gr(4, 3)  =  
gs(4, 3)  =  Suppose f is a differentiable function of x and y, and g(r, s) = f(2r − s, s2 − 7r). Use the table of values below to calculategr(4, 3) andgs(4, 3).

if x, y belong to