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Byju's Answer
Standard XII
Mathematics
Manipulation of a linear equation
Solve the mat...
Question
Solve the matrix equations:
(i)
[
x
1
]
1
0
-
2
-
3
x
5
=
0
(ii)
[
1
2
1
]
1
2
0
2
0
1
1
0
2
0
2
x
=
0
(iii)
[
x
-
5
-
1
]
1
0
2
0
2
1
2
0
3
x
4
1
=
0
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Solution
i
x
1
1
0
-
2
-
3
x
5
=
0
⇒
x
-
2
0
-
3
x
5
=
0
⇒
x
-
2
-
3
x
5
=
0
⇒
x
2
-
2
x
-
15
=
0
⇒
x
2
-
2
x
-
15
=
0
⇒
x
2
-
5
x
+
3
x
-
15
=
0
⇒
x
x
-
5
+
3
x
-
5
=
0
⇒
x
-
5
x
+
3
=
0
⇒
x
-
5
=
0
or
x
+
3
=
0
⇒
x
=
5
or
x
=
-
3
i
i
1
2
1
1
2
0
2
0
1
1
0
2
0
2
x
=
0
⇒
1
+
4
+
1
2
+
0
+
0
0
+
2
+
2
0
2
x
=
0
⇒
6
2
4
0
2
x
=
0
⇒
0
+
4
+
4
x
=
0
⇒
4
+
4
x
=
0
⇒
4
x
=
-
4
∴
x
=
-
4
4
=
-
1
i
i
i
x
-
5
-
1
1
0
2
0
2
1
2
0
3
x
4
1
=
0
⇒
x
-
0
-
2
0
-
10
-
0
2
x
-
5
-
3
x
4
1
=
0
⇒
x
-
2
-
10
2
x
-
8
x
4
1
=
0
⇒
x
2
-
2
x
-
40
+
2
x
-
8
=
0
⇒
x
2
-
48
=
0
⇒
x
2
=
48
⇒
x
=
±
48
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0
Similar questions
Q.
Solve the matrix equations:
(i)
[
x
1
]
1
0
-
2
-
3
x
5
=
0
(ii)
[
1
2
1
]
1
2
0
2
0
1
1
0
2
0
2
x
=
0
(iii)
[
x
-
5
-
1
]
1
0
2
0
2
1
2
0
3
x
4
1
=
0
Q.
Solve the following equations using factorization method.
(i)
x
2
−
3
x
−
10
=
0
(ii)
2
x
2
+
x
−
6
=
0
(iii)
√
2
x
2
+
7
x
+
5
√
2
=
0
(iv)
2
x
2
−
x
+
1
8
=
0
(v)
100
x
2
−
20
x
+
1
=
0
Q.
Solve the following matrix equation for
x
:
[
x
−
5
−
1
]
⎡
⎢
⎣
1
0
2
0
2
1
2
0
3
⎤
⎥
⎦
⎡
⎢
⎣
x
4
1
⎤
⎥
⎦
=
0
Q.
Solve the following matrix equation for
x
:
[
x
1
]
[
1
0
−
2
0
]
=
0.
Q.
If
A
=
⎡
⎢
⎣
1
−
2
1
0
−
1
1
2
0
−
3
⎤
⎥
⎦
then find
A
−
1
and hence, solve the system equations
x
−
2
y
+
z
=
0
,
−
y
+
z
=
−
2
and
2
x
−
3
z
=
10
.
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