(1) P=
(
?
1
0
1
?
1
?
1
2
1
1
?
1
)
\begin{pmatrix} -1 & 0&1 \\ -1 & -1&2\\1&1&-1 \end{pmatrix}
??1?11?0?11?12?1?
?
A=
(
1
0
1
1
1
0
?
1
2
1
)
\begin{pmatrix} 1 & 0&1 \\ 1 & 1&0\\-1&2&1 \end{pmatrix}
?11?1?012?101?
?
B=P
?
1
^{-1}
?1AP=
(
?
2
?
3
5
0
0
2
?
2
?
2
5
)
\begin{pmatrix} -2 & -3&5 \\ 0 & 0&2\\-2&-2&5 \end{pmatrix}
??20?2??30?2?525?
?
(
2
)
?
T
(
α
)
=
T
(
α
1
)
+
6
T
(
α
2
)
?
T
(
α
3
)
=
(
1
,
0
,
1
)
+
(
6
,
6
,
0
)
+
(
1
,
?
2
,
?
1
)
=
(
8
,
4
,
0
)
\begin{aligned}(2)\space T(\alpha)&=T(\alpha_1)+6T(\alpha_2)-T(\alpha_3)\\&=(1,0,1)+(6,6,0)+(1,-2,-1)\\&=(8,4,0) \end{aligned}
(2)?T(α)?=T(α1?)+6T(α2?)?T(α3?)=(1,0,1)+(6,6,0)+(1,?2,?1)=(8,4,0)?
T
(
β
)
=
T
(
e
1
)
?
T
(
e
2
)
+
T
(
e
3
)
=
(
?
2
,
?
3
,
5
)
+
(
0
,
0
,
?
2
)
+
(
?
2
,
?
2
,
5
)
=
(
?
4
,
?
5
,
8
)
\begin{aligned}T(\beta)&=T(e_1)-T(e_2)+T(e_3)\\&=(-2,-3,5)+(0,0,-2)+(-2,-2,5)\\&=(-4,-5,8) \end{aligned}
T(β)?=T(e1?)?T(e2?)+T(e3?)=(?2,?3,5)+(0,0,?2)+(?2,?2,5)=(?4,?5,8)?
注意
α
\alpha
α是行向量