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Byju's Answer
Standard XII
Mathematics
Conditional Identities
If A =2312 an...
Question
If
A
=
2
3
1
2
and
I
=
1
0
0
1
,
then find λ, μ so that A
2
= λA + μI
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Solution
Given
:
A
=
2
3
1
2
Now
,
A
2
=
A
A
⇒
A
2
=
2
3
1
2
2
3
1
2
⇒
A
2
=
4
+
3
6
+
6
2
+
2
3
+
4
⇒
A
2
=
7
12
4
7
A
2
=
λ
A
+
μ
I
⇒
7
12
4
7
=
λ
2
3
1
2
+
μ
1
0
0
1
⇒
7
12
4
7
=
2
λ
3
λ
λ
2
λ
+
μ
0
0
μ
⇒
7
12
4
7
=
2
λ
+
μ
3
λ
+
0
λ
+
0
2
λ
+
μ
⇒
7
12
4
7
=
2
λ
+
μ
3
λ
λ
2
λ
+
μ
The
corresponding
elements
of
two
equal
matrices
are
equal
.
∴
7
=
2
λ
+
μ
.
.
.
1
12
=
3
λ
⇒
λ
=
12
3
=
4
Putting
the
value
of
λ
in
eq
.
1
,
we
get
7
=
2
4
+
μ
⇒
7
-
8
=
μ
∴
μ
=
-
1
Suggest Corrections
3
Similar questions
Q.
If
A
=
2
3
1
2
and
I
=
1
0
0
1
,
then
(i) find λ, μ so that A
2
= λA + μI
(ii) prove that A
3
− 4A
2
+ A = O
Q.
If
A
=
3
1
-
1
2
and
I
=
1
0
0
1
, then find λ so that A
2
= 5A + λI.
Q.
If
A
=
2
3
1
2
, verify that
A
2
-
4
A
+
I
=
O
,
where
I
=
1
0
0
1
and
O
=
0
0
0
0
. Hence, find A
−1
.
Q.
If
A
=
3
-
2
4
-
2
, find the value of
λ
so that
A
2
=
λ
A
-
2
I
. Hence, find A
−1
.
Q.
If the vectors
−
3
i
+
4
j
+
λ
k
and
μ
i
+
8
j
+
6
k
are collinear vectors, then find
λ
and
μ
.
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