Macierze
1. DZIAŁANIA
a) A + B
d) 2A-B
1 |
1 |
-1 |
2 |
1 |
-1 |
' 5 |
2 |
3 |
0 |
1 |
-1 ■ | ||||
A = |
3 |
0 |
-2 |
B = |
3 |
1 |
-2 |
3 |
1 |
4 |
B = |
-1 |
1 |
0 | |
1 |
2 |
1 |
1 |
0 |
1 |
0 |
-2 |
1 |
1 |
0 |
1 |
1
O
-2
1
B = [ 6 2 -1 O ]
e) 3A-A —
f) 3A-A —
2. MNOŻENIE
2 B
' 7 2 3 6 '4J3 ' 3 2
B =
1 3
-2 0
-3 2 1 0
B =
0 1 1 0
-1
1
a) A =
2 2 0 1
B =
1 2 -3 0
d) A =
1 0 1 2 1 1
B =
3 2
0 -1
b) A =
0 |
1 ' |
1 |
1 -1 ‘ |
2 |
1 -1 ‘ | ||||
1 |
0 |
B = |
' 1 2 3 |
e) A = |
3 |
0 -2 |
B = |
3 |
1 -2 |
0 |
1 |
1 1 1 |
1 |
2 1 |
1 |
0 1 | |||
1 |
0 |
= 2 ‘ |
1
3
B = [ 1 0 -I]
n n
1 2 1 -3 0 1
1 |
2 |
2 ‘ |
B = |
0 |
1 |
- |
1 |
0 |
g) =
1 1 0 1
3. RÓWNANIA MACIERZOWE
1 |
2 |
3 ‘ |
( |
1 |
1 |
1 ‘ |
\ |
1 |
2 |
3 ‘ |
-1 |
2 |
1 |
-2 |
2 |
3 ‘ | |||
a) X + |
3 |
2 |
1 |
= 2 X- |
2 |
0 |
4 |
b) X • |
5 |
4 |
3 |
+ |
-3 |
3 |
-2 |
= 2X 4- X • |
5 |
1 |
3 |
1 |
1 |
1 |
V |
7 |
1 |
2 |
) |
2 |
2 |
4 |
4 |
0 |
-1 |
2 |
2 |
1 |
4. WYZNACZNIK
a) |
6 |
4 |
1 |
3 |
2 |
3 |
2 |
3 |
1 |
1 2 |
3 4 |
5 | |||||
4 |
4 |
d) |
2 |
3 |
4 |
f) |
1 |
5 |
4 |
2 |
2 0 |
0 4 |
5 | ||||
b) |
1 |
2 |
3 |
1 |
4 |
2 |
4 |
5 |
1 |
h) |
1 1 |
1 1 |
1 | ||||
2 |
1 |
1 |
2 |
3 |
4 |
6 |
5 |
4 |
2 |
2 2 |
4 1 |
0 | |||||
5 |
4 |
3 |
e) |
2 |
6 |
7 |
10 |
1 |
0 |
0 |
0 |
3 2 |
1 3 |
3 | |||
c) |
4 |
3 |
4 |
3 |
6 |
10 |
4 |
g) |
2 |
3 |
4 |
2 |
X + 1 X |
1 | |||
3 |
2 |
4 |
2 |
0 |
2 |
2 |
3 |
1 |
4 |
1 |
i) |
x2 — 1 X |
1 — X | ||||
5 |
0 |
2 |
2 |
1 |
2 |
X2 |
5. MACIERZ ODWROTNA
6 4 |
b) |
1 |
2 |
c) |
2 2 |
' 5 |
4 |
3 ' |
' 2 |
1 |
1 |
1 |
3 |
2 ' | |||
4 4 |
2 |
1 |
3 1 |
d) |
4 |
3 |
4 |
e) |
3 |
1 |
1 |
f) |
2 |
3 |
4 | ||
3 |
2 |
4 |
1 |
0 |
2 |
3 |
1 |
4 |
6. RZĄD MACIERZY
1 -1 |
2 -1 " |
1 |
1 |
1 |
1 |
c) |
3 0 6 0 |
p + 1 |
P |
p - 1 p + 7 | |||
a) |
2 -3 |
-1 1 |
b) |
2 |
2 |
3 |
-1 |
2 2 4 -1 |
d) |
P - 7 |
p — 6 |
p — 5 -10 | |
1 0 |
7 4 |
0 |
0 |
7 |
-3 |
4 |
3 |
2 11 | |||||
1 |
1 |
5 |
-3 |
7. RÓWNANIA MACIERZOWE
2 2 3 |
1 O to _1 |
' 0 2 3 |
1 to o to _1 | ||||
a) X- |
2 4 3 1 2 2 |
= x + |
1 4 3 1 1 7 |
b) |
2 2 3 1 2 1 |
•X + X = |
1 4 3 1 1 7 |