find the A-1 FOR FOLLOWING A= {-1 4 3
2 1 0 4 1 2} MAREICS
Answers
Answer:
Solution
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We have A=
⎣
⎢
⎢
⎡
1
2
0
−1
3
1
0
4
2
⎦
⎥
⎥
⎤
B=
⎣
⎢
⎢
⎡
2
−4
2
2
2
−1
−4
−4
5
⎦
⎥
⎥
⎤
Now, AB=
⎣
⎢
⎢
⎡
1
2
0
−1
3
1
0
4
2
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
2
−4
2
2
2
−1
−4
−4
5
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
2+4+0
4−12+8
0−4+4
2−2+0
4+6−4
0+2−2
−4+4+0
−8−12+20
0−4+10
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
6
0
0
0
6
0
0
0
6
⎦
⎥
⎥
⎤
=6=
⎣
⎢
⎢
⎡
1
0
0
0
1
0
0
0
1
⎦
⎥
⎥
⎤
⇒ AB=61⇒ A
−1
=
6
1
B
⇒ A
−1
=
6
1
=
⎣
⎢
⎢
⎡
2
−4
2
2
2
−1
−4
−4
5
⎦
⎥
⎥
⎤
The given system of linear equations can be written in matrix form as
AX=B, where A==
⎣
⎢
⎢
⎡
1
2
0
−1
3
1
0
4
2
⎦
⎥
⎥
⎤
,X=
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
,B=
⎣
⎢
⎢
⎡
3
17
7
⎦
⎥
⎥
⎤
⇒ X=A
−1
B
⇒ X=
6
1
=
⎣
⎢
⎢
⎡
2
−4
2
2
2
−1
−4
−4
5
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
3
17
7
⎦
⎥
⎥
⎤
⇒ X=
6
1
=
⎣
⎢
⎢
⎡
2×3+2×17−4×7
−4×3+2×17−4×7
2×3−1×17+5×7
⎦
⎥
⎥
⎤
⇒ X=
6
1
=
⎣
⎢
⎢
⎡
6+34−28
−12+34−28
6−17+35
⎦
⎥
⎥
⎤
⇒ =
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
6
1
=
⎣
⎢
⎢
⎡
12
−6
24
⎦
⎥
⎥
⎤
⇒ =
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
2
−1
4
⎦
⎥
⎥
⎤
⇒ x=2,y=−1 and z=4