If a is a 2x2 matrix such that |3a| 108 then |a| is?
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Answered by
0
Answer:
36/0 -32/4
Step-by-step explanation:
Correct option is
D
[
36
0
−32
4
]
A⋅[
1
0
2
3
] is a scalar matrix and ∣3A∣=108
Let the scalar matrix be [
k
0
0
k
]
A⋅[
1
0
2
3
]=[
k
0
0
k
]
A=[
k
0
0
k
][
1
0
2
3
]
−1
⟹A=[
k
0
0
k
][
1
0
−2/3
1/3
]
⟹A=[
k
0
−2k/3
k/3
]
∣A∣=
3
k
2
∣3A∣=108
As we know kA∣=k
n
∣A∣
∣3A∣=3
2
3
k
2
⟹k
2
=36⟹k=±6
So, putting the value of k in the matrix A
A=[
6
0
(−2/3)(6)
6/3
]
A=[
6
0
−4
2
]
So, A
2
=[
6
0
−4
2
][
6
0
−4
2
]
⟹A
2
=[
36
0
−32
4
]
Hence, this is the answer.
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