Q. 13

# If <span lang="EN

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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