Wydział: WiLiŚ, Budownictwo i Transport, sem.1
dr Jolanta Dymkowska
Rachunek macierzowy
A =
2
3
1
0
B =
1
4
−1
1
C =
2
6
−4
0
D =
1
1
0
−1
2
1
E =
3
7
−2
0
1
2
F =
1
−4
0
1
1
2
G =
1
2
0
−1
5
−1
3
0
1
H =
2
1
0
1
1
2
−1
2
1
J =
3
1
−2
3
−2
4
−3
5
−1
K =
0
3
0
5
2
−2
0
4
3
1
0
6
0
−2
5
0
L =
3
3
3
−3
−2
1
2
5
2
1
4
1
0
2
0
−2
M =
1
5
2
0
−2
0
2
0
2
3
0
5
Zad.1 Obliczyć: 3A + B , B − 2C , 5D + F
T
, CE , AB + BC , FH
T
, E
T
G , HJ − JH , 4K + L
T
, GM , KM
T
,
(A − 2C)D , F(2C − 3B) , EF + A
2
, (FE + G)
T
.
Zad.2 Obliczyć: det A , det B , det C , det G , det H , det(FE) , det J , det K , det L .
Zad.3 Obliczyć: A
−1
, B
−1
, (C
−1
+ C)
−1
, G
−1
, (EF)
−1
, H
−1
, K
−1
, (M
T
M)
−1
.
Zad.4 Oblicz wyznaczniki:
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
0
0
4
−2
5
6
5
−1
0
−5
3
5
2
1
2
3
−3
4
2
1
−1
2
6
2
1
0
2
3
0
−5
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
5
6
0
0
0
1
5
6
0
0
0
1
5
6
0
0
0
0
1
5
6
0
0
1
5
1
3
2
1
4
2
1
5
1
2
3
4
1
0
1
2
1
1
5
2
3
−1
1
−1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
2
1
4
3
5
3
5
6
8
7
4
2
8
9
7
6
0
0
2
3
5
4
0
0
4
3
0
0
0
0
6
5
0
0
0
0
Zad.5 Rozwiąż równanie macierzowe:
a) 2A + 3X = B
A =
2
1
1
−3
0
2
B =
3
4
6
1
2
1
b) 5A − X = 3B
A =
1
5
2
3
0
1
4
1
5
B =
2
7
0
0
1
4
5
6
0
c) AX = B
A =
2
−1
1
1
3
1
2
1
1
B =
1
0
1
−2
0
3
1
1
0
d) XA = B
A =
3
−2
5
−4
B =
−1
2
−5
6
e) XA = B
A =
1
1
−1
2
1
0
1
−1
1
B =
h
1
2
3
i
f) AX − B = X
A =
2
1
3
3
B =
2
1
5
0
3
2
g) XA − 2X = B
A =
2
−1
1
1
3
1
2
1
2
B =
1
0
2
2
4
0
h) AXB + 2AX = C
A =
0
1
1
1
0
0
1
0
1
B =
1
−1
1
1
C =
0
1
1
0
1
1
Zad.6 Wyznacz rząd macierzy:
A =
2
−6
−4
−3
9
9
B =
1
1
1
1
1
2
C =
1
3
2
0
2
6
4
0
2
D =
0
1
−2
−1
0
3
2
−3
0
E =
1
3
4
2
−1
0
4
2
8
F =
1
1
−1
−1
−1
1
1
1
−1
G =
2
−1
3
0
4
−2
6
0
5
0
1
2
H =
2
1
−1
3
6
3
−3
9
8
4
−4
12
J =
1
−1
0
2
1
3
1
1
3
2
−1
−3
−1
1
0
K =
1
1
1
1
2
2
3
−1
0
0
1
−3
3
3
5
−3
L =
1
2
−1
−1
3
0
2
−1
−7
−1
1
−4
M =
2
3
0
4
1
−1
1
2
5
0
4
−2
1
−1
2
2
N =
2
1
1
1
−2
1
2
3
−1
2
3
0
1
−3
−2
2
4
6
−2
4
P =
1
3
−2
−3
2
4
2
2
1
−1
2
5
1
−1
3
2
0
1
3
1
4
1
2
6
3