110
3. Wyznaczyć macierz X = A B + 3C dla
'0 |
-1 |
r |
2 |
i' | ||
1 |
2 |
i |
, B = |
0 |
es ii |
0 |
1 |
0 |
—i <M 1 |
-1 T—( 1 _1 |
i 1 Co i_ |
Obliczmy iloczyn
Zatem
AB =
AB + 3C
-1
1
4
+ 3
1
0
-3
-1 1
2 1
0 -2
2' |
'-ii | ||
0 |
= |
i | |
- |
-1 |
4 | |
-i |
3 |
1
4
2
1
-5
1 1 |
1 1 |
1 1 |
1 2 |
1 1 |
1 3 | |||||
0 1 |
0 1 |
0 1 |
0 1 |
0 1 |
0 1 |
Obliczmy A3 = A2-A =
oraz
B2
BB =
'1 -1 |
1 -1 |
-1 —2 | ||
2 1 |
2 1 |
-1 tH 1 |
Stąd mamy
Z = A3 + B2
1 3 0 1
-1 -2 4 -1
0 1
4 0
1. Dane są macierze: A =
'1 |
2 |
2 |
r | |
0 |
1 |
, B = |
-1 |
2 |
3 |
1 |
0 |
1 |
. Znaleźć taką macierz
2. Dane są macierze A =
3 12 -10 3
4 2 1
B =
1 2 3 4 0 1 -12 2
C =
D =
Znaleźć: (a) C',
(e) C D, (f)D\
(b) 3,4 - 2B, (c) AT - Br, (d) (2A - B)-C,
3. Dla danych macierzy: A =
(a) A B, (b) B-A.
4. Niech
B =
wyznaczyć:
' 2 -3 —5 |
-1 3 5' |
2 -2 -4' | |||
A = |
-14 5 |
, B = |
1 -3 -5 |
, c = |
-13 4 |
1 -3 -4 |
-13 5 |
1 -2 -3 |
Pokazać, że (a) A-B = B-A = O, (b) A-C — A, (c) C-zł — C.
5. Wyznaczyć macierze:
(a)
= I.
(b)
1 0
-1 -1
0 1
2 1 |
7r |
n/2 1 |
0 3 |
-V2 |
1 |
0 1 |
i |
1 |
1 3 |
0 |
1 |
= |
0 |
0 |
-1 |
-1 |
-1 |
1- | |
1 |
0 | |
0 |
1 | |
.1 |
1. |
2 10 0 0 2 0 0 0 0 3 1 .0 0 0 3
6. Pokazać, że
7. Niech
-1 |
0 |
2 |
1 |
3 |
4 |
B = [ 1 2 3]T, C = [-1 2 3].