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Question
Find A2−5A+611 if A=⎡⎢⎣2012131−10⎤⎥⎦
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Solution
Let the problem,We have to given A=⎡⎢⎣2012131−10⎤⎥⎦Now, we have to calculate,A2−5A+6I ------ (i)
For this A2=⎡⎢⎣2012131−10⎤⎥⎦⎡⎢⎣2012131−10⎤⎥⎦=⎡⎢⎣5129−250−1−2⎤⎥⎦Now, from (i)
=⎡⎢⎣5129−250−1−2⎤⎥⎦−5⎡⎢⎣2012131−10⎤⎥⎦+6⎡⎢⎣100010001⎤⎥⎦
==⎡⎢⎣5129−250−1−2⎤⎥⎦−⎡⎢⎣1005105155−50⎤⎥⎦+⎡⎢⎣600060006⎤⎥⎦
=⎡⎢⎣11129450−14⎤⎥⎦−⎡⎢⎣1005105155−50⎤⎥⎦
=⎡⎢⎣11−3−1−1−10−544⎤⎥⎦Hence A2−5A+6I=⎡⎢⎣11−3−1−1−10−544⎤⎥⎦
We have to given A=⎡⎢⎣2012131−10⎤⎥⎦
Now,
we have to calculate,
A2−5A+6I ------ (i)
For this A2=⎡⎢⎣2012131−10⎤⎥⎦⎡⎢⎣2012131−10⎤⎥⎦=⎡⎢⎣5129−250−1−2⎤⎥⎦
Now, from (i)
=⎡⎢⎣5129−250−1−2⎤⎥⎦−5⎡⎢⎣2012131−10⎤⎥⎦+6⎡⎢⎣100010001⎤⎥⎦
==⎡⎢⎣5129−250−1−2⎤⎥⎦−⎡⎢⎣1005105155−50⎤⎥⎦+⎡⎢⎣600060006⎤⎥⎦
=⎡⎢⎣11129450−14⎤⎥⎦−⎡⎢⎣1005105155−50⎤⎥⎦
=⎡⎢⎣11−3−1−1−10−544⎤⎥⎦
Hence A2−5A+6I=⎡⎢⎣11−3−1−1−10−544⎤⎥⎦
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