Q.
If A=−4 −13 1 then the determinant line matrix A2016−2A2015−A2014, is
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a
2014
b
2016
c
-175
d
-25
answer is B.
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Detailed Solution
Let B=A2016−2A2015−A2014 Then ,B=A2014A2−2A−I⇒ |B|=|A|2014A2−2A−INow, A−−4 −13 1∴A2−2A−I=−4−131−4−131−2−4−131−1001=133−9−2+82−6−2+−100−1=205−15−5⇒ A2−2A−I=205−15−5=−25and |A|=−4 −13 1=−1 Hence, |B|=(−1)2014=−25
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