SchoolofMathematicsandStatistics
TeKuraataiTatauranga
STAT391TutorialWeek5,2021
1.Considerasymmetricmatrix
A
=
21
12
:
Showthat
(a)Theeigenvalues
i
andthecorrespondingeigenvectors
e
i
,
i
=1
;
2are
1
=3
;
2
=1
and
e
1
=
1
p
2
1
1
and
e
2
=
1
p
2
1
1
;
(b)
e
1
and
e
2
are
independent
,
(c)
A
=
1
e
1
e
>
1
+
2
e
2
e
>
2
,
(d)
A
1
=
1
1
e
1
e
>
1
+
1
2
e
2
e
>
2
,
(e)
j
A
j
=
1
2
,
(f)trace(
A
)=
1
+
2
,
2.Thinkofamatrix
A
m
n
asa
lineartransformation
ofavector
x
in
R
n
toavec...
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