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 A3 Given:
5A=[3−44x]
Dividing both sides by 5
A=⎡⎢
⎢
⎢⎣35−4545x5⎤⎥
⎥
⎥⎦
It is given that AAT=ATA=I where , I= Identity matrix Using property of transpose. AT=⎡⎢
⎢
⎢⎣3545−45x5⎤⎥
⎥
⎥⎦ AAT=⎡⎢
⎢
⎢⎣35×35+45×4535×45−45×x545×35−x5×4545×45+x5×x5⎤⎥
⎥
⎥⎦ ⇒AAT=⎡⎢
⎢
⎢⎣14(3−x)254(3−x)2516+x225⎤⎥
⎥
⎥⎦
But,
AAT=I=[1001]
So, comparing the corresponding terms, 425(3−x)=0 ⇒x=3