The standard basis â—»={e_(1),e_(2)} and a custom basis â—»={b_(1),b_(2)} for R^(2) are shown in the figures below.
Standard hacic a. a.
Standardbasis={e,e} y
-2-1
23
[id] t
b2
Custom basis={b,b}
a.What are the custom -coordinates of the basis vectors b and b? Enter your answers as a vectors of the form <1,2>
[b]= <1,0>
[b]= <0,1>
b.What are the standard -coordinates of the basis vectors b and b? Enter your answers as a vectors of the form <1,2>
[b]= <-3,2>
[b]=<1,1>
c.Find the change of basis matrix from custom -coordinates to standard -coordinates
[id]
d. Find the change of basis matrix from standard -coordinates to custom -coordinates
-1/5
1/5
[id]
2/5
3/5
e.Find the -coordinates of the vector 5b+7b.Enter your answer as a vector of the form<1,2>
[5b+7b]= <-8,17>
f.Find the-coordinates of the vector-4e+5e.Enter your answer as a vector of the form<1,2>
[-4e+5e]= <-4,5>
