solve the following system of linear equations by matrix method. x-2y+2z=7 2x-y+3z=12 3x+2y-z=5
Answers
Answer:
x=1, y=2, z= 3 hope it is correct
Step-by-step explanation:
Let A=
⎣
⎢
⎢
⎡
1
3
2
−1
4
−1
2
−5
3
⎦
⎥
⎥
⎤
B=
⎣
⎢
⎢
⎡
7
−5
12
⎦
⎥
⎥
⎤
X=
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
Find ∣A∣
∣A∣=
∣
∣
∣
∣
∣
∣
∣
∣
1
3
2
−1
4
−1
2
−5
3
∣
∣
∣
∣
∣
∣
∣
∣
=1(12−5)+1(9+10)+2(−3−8)
=7+19−22=26−22=4
=0
A exists
To find cofactors of A
A
11
=+
∣
∣
∣
∣
∣
∣
4
−1
−5
3
∣
∣
∣
∣
∣
∣
=7 A
21
=−
∣
∣
∣
∣
∣
∣
−1
−1
2
3
∣
∣
∣
∣
∣
∣
=+1 A
31
=+
∣
∣
∣
∣
∣
∣
−1
4
2
−5
∣
∣
∣
∣
∣
∣
=−3
A
12
=−
∣
∣
∣
∣
∣
∣
3
2
5
3
∣
∣
∣
∣
∣
∣
=−19 A
22
=+
∣
∣
∣
∣
∣
∣
1
2
2
3
∣
∣
∣
∣
∣
∣
=−1 A
32
=−
∣
∣
∣
∣
∣
∣
1
3
2
5
∣
∣
∣
∣
∣
∣
=+11
A
13
=+
∣
∣
∣
∣
∣
∣
3
2
4
−1
∣
∣
∣
∣
∣
∣
=−11 A
23
=−
∣
∣
∣
∣
∣
∣
1
2
−1
−1
∣
∣
∣
∣
∣
∣
=−1 A
33
=+
∣
∣
∣
∣
∣
∣
1
3
−1
4
∣
∣
∣
∣
∣
∣
=7
∴Cofactor matrix=
⎣
⎢
⎢
⎡
7
1
3
−19
−1
11
−11
0
7
⎦
⎥
⎥
⎤
adj A=
⎣
⎢
⎢
⎡
7
1
−3
−19
−1
11
−11
−1
7
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
7
−19
−11
1
−1
−1
−3
11
7
⎦
⎥
⎥
⎤
∴A=
∣A∣
adj A
=
4
1
⎣
⎢
⎢
⎡
7
−19
−11
1
−1
−1
3
11
7
⎦
⎥
⎥
⎤
∴X=A B=
4
1
⎣
⎢
⎢
⎡
7
−19
−11
1
−1
−1
3
11
7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
7
−5
12
⎦
⎥
⎥
⎤
=
4
1
⎣
⎢
⎢
⎡
49−5−36
−133+5+132
−77+5+84
⎦
⎥
⎥
⎤
=
4
1
⎣
⎢
⎢
⎡
8
4
12
⎦
⎥
⎥
⎤
∴X=[1]⇒x=2;y=1;z=3.