Consider the bases B = left(begin{array}{c}begin{bmatrix}2

aortiH 2020-11-14 Answered

Consider the bases B=([23],[35])ofR2 and C=([110],[101],[011])ofR3.
and the linear maps SL(R2,R3) and TL(R3,R2) given given (with respect to the standard bases) by [S]E,E=[215332] and [T]E,E=[111111] Find each of the following coordinate representations. (b)[S]E,C
(c)[S]B,C

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Expert Answer

Caren
Answered 2020-11-15 Author has 96 answers

B=([23],[35])ofR2,C=([110],[101],[011])ofR3.

SL(R2,R3),TL(R3,R2)
[S]E,E=[215332],[T]E,E=[111111]

(b) To find [S]E,C:
S([10])=[253]=a[110]+b[101]+c[011]=[a+ba+cb+c]
a+b=2,a+c=5,b+c=3
b=2ab+c=2a+c=3a+c=5
a+c=5+a+c=52c=0c=0,b=3,a=5a=5,b=3,c=0
S([01])=[132]=a[110]+b[101]+c[011]=[a+ba+cb+c]
a+b=1,a+c=3,b+c=2
b=1ab+c=1a+c=2a+c=3
a+c=3+a+c=32c=0c=0,a=3,b=2a=3,b=2,c=0
[S]E,C=[533200]

c) To find [S]B,C

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