ROZDZIAŁ 7. PRZEKSZTAŁCENIE LINIOWE
|
"i 0' | |
|
. M£(y/) = |
2 0 |
|
- |
3 0 |
c) Ma{(p)
-1 J 1 -I
|
" " . ' ■ ...... |
'2 r |
"l 0" |
3 2 |
" 1 |
0 |
0" | |||
|
A = A-' ' |
1 T - . J |
, B = |
i i |
, c= |
\ lj |
’ D = |
1 |
-1 |
0 |
|
-1 |
1 |
-1 |
|
"2 |
2. |
i i - |
-1 |
G" | |||||||||
|
d):M*(<») = |
1 |
-i |
" |
Mg(r)= |
-1 |
1 |
0 |
5 | |||||
|
0 |
4j |
A ;'A yi |
1 - |
1 |
0 | ||||||||
|
~i r |
r-3 |
0 0’ |
~2 |
1 |
0" |
% |
0 |
0^ | |||||
|
A = |
i i |
5 - |
B = |
1 |
-1 0 |
, c- |
1 |
1 |
0 |
? D = |
0 |
3 |
l |
|
-1 |
1 -1 |
0 |
0 |
-1 |
0 |
2 |
1 | ||||||
7.11. Dane są macierze M£(», Mg {w) przekształceń liniowych <p:R!! RA', y/: R* -» R” i bazy A, B, C, D. Znaleźć Ker^ Ker^, Ker(^o^), Ker(^ o (p) oraz \m<p, \my/, Im(cp ■? y/\ \m(y/ ° ę).
a)
A =
1 (
0 ( 0 1
7.12. Dane są mac y/\ R3 —> R? kształceniem
a) M£(#) =
A =
1 1 2 0 -I 1
' 1 1 1] -1 0 1
|
-v |
'1 |
2 |
2 |
t |
l |
r |
5j- | ||
|
, B = |
1 |
1 |
-1 |
, c = |
i |
0 |
-i |
; d y |
‘ 1 0' |
|
0 |
0 |
h |
mmM |
i |
i |
: o |
:-i i_ |
b) Mf(A=
|
~ 0 |
0 |
0“ |
- |
"0 |
i |
0" | ||
|
-i |
0 |
0 |
. Mg(r) |
o |
0 |
0 | ||
|
i |
0 |
0 - |
1 |
1 | ||||
|
i o o |
‘i i r |
j |
1 | |||||
|
1 0 |
? |
B |
0 1 1 |
, C = |
0 |
0 | ||
|
1 1 |
1 o o lT_ |
0 |
1 | |||||
D =
0 1 0'
I 0 o
II 1
1 ( 1 0
b) Mb(^) =
• :;a =
A -
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