Q. 13

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Answer :

We have,



Expanding it along R1 to get,


1(a2×a – 1× 1) – a (a× a – a2 × 1) + a2 (a× 1 – a2× a2) = - 4


(a3 – 1) – a (a2 – a2) + a2 (a – a4) = - 4


(a3 – 1) – a (0) + a2 (a – a4) = - 4


(a3 – 1) + a2 (a – a4) = - 4


(a3 – 1) + a2× a (1 – a3) = - 4


(a3 – 1) + a3 (1 – a3) = - 4


(a3 – 1) - a3 (a3 - 1) = - 4


(a3 – 1) (1 - a3)= - 4


-(1 - a3)(1 - a3)= - 4


-(1 - a3)2= - 4


(1 - a3)2= 4 ….. (1)


Now in


Expand along R1 to get,


= (a3 – 1) [ (a – a4) × 0 - (a3 – 1) (a3 – 1)] – 0[ 0 × 0 -(a – a4) (a3 – 1)] + (a – a4) [0× (a3 – 1)- (a – a4) (a – a4)]


= (a3 – 1) [ 0 - (a3 – 1)2] – 0[ 0 -(a – a4) (a3 – 1)] + (a – a4) [0 - (a – a4)2]


= - (a3 – 1)3 – (a – a4)3


= - (a3 – 1)3 – (a (1 – a3))3


= - (a3 – 1)3 – a3 (1 – a3)3


= - ((-1)3 (1 – a3))3 – a3 (1 – a3)3


= - (-1) (1 – a3))3 – a3 (1 – a3)3


= (1 – a3)3 – a3 (1 – a3)3


= (1 – a3)3 (1 – a3)


= (1 – a3)4


= ((1 - a3)2)2


From (1)


= (4)2


= 16


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