Solve the following system of equations by matrix method
3x - 2y + 3z = 8
2x + y – z = 1
4x - 3y + 2z = 4
Answers
Answer:
ANSWER
x−2y=10.....(1)
2x+y+3z=8.....(2)
−2y+z=7.....(3)
A=
⎣
⎢
⎢
⎡
1
2
0
−2
1
−2
0
3
1
⎦
⎥
⎥
⎤
,X=
⎣
⎢
⎢
⎡
10
8
7
⎦
⎥
⎥
⎤
∣A∣=1(1+6)+2(2−0)+0
=7+4=11
=0
∴A
−1
exists
a
11
=[
1
−1
3
]=(1+6)=7,a
12
=−[
2
0
3
1
]=−2,a
13
=[
2
0
1
−2
]=−4
a
21
=−[
−2
−2
0
1
]=−(−2)=2,a
22
=[
1
0
0
1
]=1,a
23
=−[
1
0
−2
−2
]=−(−2)=2
a
31
=[
−2
1
0
3
]=−6,a
32
=−[
1
2
0
3
]=−(3)=−3,a
33
=[
1
2
−2
1
]=1+4=5
∴adj A=
⎣
⎢
⎢
⎡
7
2
−6
−2
1
−3
−4
2
5
⎦
⎥
⎥
⎤
T
=
⎣
⎢
⎢
⎡
7
−2
−4
2
1
2
−6
−3
5
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
adj A
=
11
1
⎣
⎢
⎢
⎡
7
−2
−4
2
1
2
−6
−3
5
⎦
⎥
⎥
⎤
AX=B⇒X=A
−1
B
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
11
1
⎣
⎢
⎢
⎡
7
−2
−4
2
1
2
−6
−3
5
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
10
8
7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
11
1
⎣
⎢
⎢
⎡
70+16−42
−20+8−21
−40+16+35
⎦
⎥
⎥
⎤
=
11
1
⎣
⎢
⎢
⎡
44
−33
11
⎦
⎥
⎥
⎤
⇒x=4,y=−3,z=1
Answer:
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