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Question

If 5A=(3−44x) and AAT=ATA=I, then the value of x, is

A
3
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B
3
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C
2
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D
2
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Solution

The correct option is A 3
Given:
5A=[344x]
Dividing both sides by 5
A=⎢ ⎢ ⎢354545x5⎥ ⎥ ⎥

It is given that
AAT=ATA=I
where , I= Identity matrix
Using property of transpose.
AT=⎢ ⎢ ⎢354545x5⎥ ⎥ ⎥
AAT=⎢ ⎢ ⎢35×35+45×4535×4545×x545×35x5×4545×45+x5×x5⎥ ⎥ ⎥
AAT=⎢ ⎢ ⎢14(3x)254(3x)2516+x225⎥ ⎥ ⎥
But,
AAT=I=[1001]
So, comparing the corresponding terms,
425(3x)=0
x=3

Hence, option A.

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