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Byju's Answer
Standard XII
Mathematics
Finding Inverse Using Elementary Transformations
Solve system ...
Question
Solve system of linear equations, using matrix method.
2
x
+
y
+
z
=
−
1
,
x
−
2
y
−
z
=
3
2
,
3
y
−
5
z
=
9
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Solution
2
x
+
y
+
z
=
−
1
x
−
2
y
−
z
=
3
2
3
y
−
5
z
=
9
⎡
⎢
⎣
2
1
1
1
−
2
−
1
0
3
−
5
⎤
⎥
⎦
⎡
⎢
⎣
x
y
z
⎤
⎥
⎦
=
⎡
⎢
⎣
−
1
3
/
2
9
⎤
⎥
⎦
A
B
C
A
X
=
B
X
=
A
−
1
B
A
−
1
=
A
d
j
(
A
)
|
A
|
|
A
|
=
2
[
10
+
3
]
−
1
[
−
5
]
+
1
[
3
]
=
26
+
5
+
3
=
34
A
d
j
(
A
)
=
⎡
⎢
⎣
A
11
A
12
A
13
A
21
A
22
A
23
A
31
A
32
A
33
⎤
⎥
⎦
T
A
11
=
∣
∣
∣
−
2
−
1
3
−
5
∣
∣
∣
(
−
1
)
1
+
1
=
13
A
12
=
∣
∣
∣
1
−
1
0
−
5
∣
∣
∣
(
−
1
)
1
+
2
=
−
5
A
13
=
(
−
1
)
1
+
3
∣
∣
∣
1
−
2
0
3
∣
∣
∣
=
3
A
21
=
(
−
1
)
2
+
1
∣
∣
∣
1
1
3
−
5
∣
∣
∣
=
8
A
22
=
(
−
1
)
2
+
2
∣
∣
∣
1
−
1
0
−
5
∣
∣
∣
=
−
5
A
23
=
(
−
1
)
2
+
3
∣
∣
∣
2
1
0
3
∣
∣
∣
=
−
6
A
31
=
(
−
1
)
3
+
1
∣
∣
∣
1
1
−
2
−
1
∣
∣
∣
=
1
A
32
=
(
−
1
)
3
+
2
∣
∣
∣
2
1
1
−
1
∣
∣
∣
=
3
A
33
=
(
−
1
)
3
+
3
∣
∣
∣
2
1
1
−
2
∣
∣
∣
=
−
5
⎡
⎢
⎣
x
y
z
⎤
⎥
⎦
=
1
34
⎡
⎢
⎣
13
8
1
−
5
−
5
3
3
−
6
−
5
⎤
⎥
⎦
⎡
⎢
⎣
−
1
3
/
2
9
⎤
⎥
⎦
⎡
⎢
⎣
x
y
z
⎤
⎥
⎦
=
1
34
⎡
⎢ ⎢ ⎢
⎣
−
13
+
12
+
9
5
−
15
2
+
27
−
3
−
9
−
45
⎤
⎥ ⎥ ⎥
⎦
x
=
8
34
,
y
=
24.5
34
,
z
=
−
57
34
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Q.
Solve the system of equations, using matrix method
2
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