Matrix representation of a linear transformation
Recall the standard basis E={vec(e)_(1),vec(e)_(2)} in R^(2) where
vec(e)_(1)=([1],[0]),vec(e)_(2)=([0],[1]).
The linear transformation phi :R^(2)->R^(2) is defined as
phi ([x_(1)],[x_(2)])=([-x_(2)],[x_(1)+2x_(2)])
Tasks
(a) What is the matrix representation of phi from the standard basis to the standard basis?
R_(E->E)(phi )=(â—»)
(b) Suppose basis B={vec(b)_(1),vec(b)_(2)} in R^(2) is
vec(b)_(1)=([7],[-4]),vec(b)_(2)=([2],[-1]),
what is the matrix representation of phi from basis B to basis B ?
R_(B->B)(phi )=(â—»)
Hint: id
Matrix representation of a linear transformation Recall the standard basis E={e,e2} in R2 where
The linear transformation : IR2 > R2 is defined as
Tasks
(a) What is the matrix representation of from the standard basis to the standard basis?
REE
(b) Suppose basis B={b1,bz} in R2 is
what is the matrix representation of from basis B to basis B
RB=B(
Hint: RE(id) is trivial to find.
cFind a basis G={gg} such that the matrix representation of from basis G to basis G is
-29
RG G(
36
31
gi
g2