Math, asked by jatinparmar412, 22 days ago

If a is a 2x2 matrix such that |3a| 108 then |a| is?​

Answers

Answered by rsgopika1067
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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