inverse of the matrix A
AA-1 =A-1 A=E
simultaneous linear algebraic equations
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Category: mathematicsmathematics

Inverse of the matrix A

1. inverse of the matrix A

INVERSE OF THE MATRIX A

2. AA-1 =A-1 A=E

A A-1 =A-1 A=E

3.

A2 2
2
5
10 6
5
2
10
6
10 0
A11 6
A21 2
A12 10
A22 5
1
1
6
2 0,6 0,2
1 6 2
1
10
10
A
1
1
10 10 5 10
5 1 0,5
10
10

4.

A3 3
1
8
9
2
9
9
1 2
8
9
9
9
0
0
1
0
0 25 0
1
A11 9
A21 2
A31 0
A12 8
A22 1
A32 0
A13 9
A23 27
A33 25
1
1
1
( 2) 0
9
25
25
25 0,36 0,08
0
9 2 0
1
1
1
1
1
A
8
1
0 8
1
0 0,32 0,04 0
25
25
25
25
0,36 1,08 1
1
1
9 27 25 1
( 9) 27 25
25
25
25

5. simultaneous linear algebraic equations

SIMULTANEOUS LINEAR ALGEBRAIC EQUATIONS
a11 x1 a12 x2 ... a1n xn b1
a x a x ... a x b
21 1 22 2
2n n
2
am1 x1 am 2 x2 ... amn xn bm
a11
a21
a
m1
a12
a22
am 2
a1n x1 b1
a2 n x2 b2
amn xn bm

6.

a11
a21
A
a
m1
a12
a22
am 2
a1n
a2 n
amn
AX B
x1
x2
X
x
n
a11
~ a21
A
a
m1
a12
a22
am 2
b1
b2
B
b
m
a1n b1
a2 n b2
amn bm

7.

Cramer
a11 x1 a12 x2 ... a1n xn b1
a x a x ... a x b
21 1
22 2
2n n
2
an1 x1 an 2 x2 ... ann xn bn
x1
a1n
b1
a12
b2
a22 a2 n
bn
a11
x2
an 2 ann
x1
x2
a21
a22 a2 n
x2
xn
xn
a11
a12 b1
a21
a22 b2
an1
xn
an 2 ann
an1
an1 bn ann
x1
a12 a1n
b1 a1n
a21 b2 a2 n
a11
an 2 bn

8.

4 x 5 y 8
3 x 2 y 7
x
8 5
7
2
51
x
51
x
23
y
4
5
3 2
23 0
4
8
3
7
y
4
4
y
23

9.

9 9 6
10 5 5 9
8 2 3
6 9 9
9 5 5 51
3
2 1
1
9 9
10 5 5 85 0
8
1
2 1
6 9
10 9 5 102
8
3
1
1
9 6
10 5 9 51
8
2
3
102
51
51
0,6;
1,2;
0,6
85
85
85

10.

8a 5b 8c 6d 4
4a 3b 8c 5d 10
5a 7b 4d 2
4a 8b 8c 5d 7
4
a
5 8
c
8
5
5
7
0
4
4 8 8
6
4
10
8
5
5
2
0
4
4
7
8
5
2
7
0
4
184
b
5
4
6
4
3
10
5
5
7
2
4
7
5
8 5 8
343
d
56
4
4
3
8
10
5
7
0
2
4 8 8
200 0
5
8
5
4 8
3
4
8
8 5
4
8
3
8 8
6
6
10
7
8 5 8
32
7
a 184
56
343
32
0,92; b b
0,28; c c
1,715; d d
0,16
200
200
200
200
a 0,92; b 0,28; c 1,715; d 0,16. Answer : (0,92;0,28; 1,715; 0,16)
a
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