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Question
If A=⎡⎢⎣144414441⎤⎥⎦, then A2−6A= _____.
If A=⎡⎢⎣144414441⎤⎥⎦, then A2−6A= _____.
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Solution
The correct option is A 27I3
Given, A=⎡⎢⎣144414441⎤⎥⎦Therefore, A2=⎡⎢⎣144414441⎤⎥⎦⎡⎢⎣144414441⎤⎥⎦=⎡⎢⎣1+16+164+4+164+16+44+4+1616+1+1616+4+44+16+416+4+416+16+1⎤⎥⎦=⎡⎢⎣332424243324242433⎤⎥⎦and 6A=⎡⎢⎣144414441⎤⎥⎦=⎡⎢⎣624242462424246⎤⎥⎦Thus A2−6A =⎡⎢⎣332424243324242433⎤⎥⎦ −⎡⎢⎣624242462424246⎤⎥⎦=⎡⎢⎣33−624−2424−2424−2433−624−2424−2424−2433−6⎤⎥⎦=⎡⎢⎣270002700027⎤⎥⎦=27I3
Given, A=⎡⎢⎣144414441⎤⎥⎦
Therefore, A2=⎡⎢⎣144414441⎤⎥⎦⎡⎢⎣144414441⎤⎥⎦
=⎡⎢⎣1+16+164+4+164+16+44+4+1616+1+1616+4+44+16+416+4+416+16+1⎤⎥⎦
=⎡⎢⎣332424243324242433⎤⎥⎦
and 6A=⎡⎢⎣144414441⎤⎥⎦
=⎡⎢⎣624242462424246⎤⎥⎦
Thus A2−6A =⎡⎢⎣332424243324242433⎤⎥⎦ −⎡⎢⎣624242462424246⎤⎥⎦
=⎡⎢⎣33−624−2424−2424−2433−624−2424−2424−2433−6⎤⎥⎦
=⎡⎢⎣270002700027⎤⎥⎦
=27I3
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