Consider the following vectors in
R
3
R
3
:
α
1
=
(
1
,
0
,
0
)
α
1
=(1,0,0)
α
2
=
(
1
,
0
,
1
)
α
2
=(1,0,1)
α
3
=
(
0
,
1
,
0
)
α
3
=(0,1,0)
α
4
=
(
−
2
,
3
,
1
)
α
4
=(−2,3,1)
β
1
=
(
1
,
0
,
2
)
β
1
=(1,0,2)
β
2
=
(
0
,
1
,
1
)
β
2
=(0,1,1)
β
3
=
(
1
,
−
4
,
0
)
β
3
=(1,−4,0)
β
4
=
(
1
,
3
,
1
)
β
4
=(1,3,1)
Determine if there is a linear transformation
T
:
R
3
→
R
3
T:R
3
→R
3
such that
T
α
i
=
β
i
Tα
i
=β
i
for
i
=
1
,
2
,
3
,
4
i=1,2,3,4.
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