Let A=[a b c p q r x y z] and suppose that det.(A)=2 then the det.(B) equals, where B=[4 x 2 a -p 4 y 2 b -q 4 z 2 c -r]

Question

Let A=[a b c p q r x y z] and suppose that det.(A)=2 then the det.(B) equals, where B=[4 x 2 a -p 4 y 2 b -q 4 z 2 c -r] (A)  operatornamedet( B )=-2 (B)  operatornamedet( B )=-8 (C)  operatornamedet(B)=-16 (D)  operatornamedet( B )=8

Tardigrade Admin · Accepted Answer

operatornamedet( B )=|4 x 2 a - p 4 y 2 b - q 4 z 2 c - r |=(4)(2)(-1)| x a p y b q z c r |=-8| x y z a b c p q r |=-8| a b c p q r x y z | =-8 × 2=-16

Q. Let $A = ⎣ ⎡ a p x b q y c r z ⎦ ⎤$ and suppose that det.(A)=2 then the det.(B) equals, where $B = ⎣ ⎡ 4 x 4 y 4 z 2 a 2 b 2 c - p - q - r ⎦ ⎤$

$det (B) = - 2$

$det (B) = - 8$

$det (B) = - 16$

$det (B) = 8$

$det (B) = ∣ ∣ 4 x 4 y 4 z 2 a 2 b 2 c - p - q - r ∣ ∣ = (4) (2) (- 1) ∣ ∣ x y z a b c p q r ∣ ∣ = - 8 ∣ ∣ x a p y b q z c r ∣ ∣ = - 8 ∣ ∣ a p x b q y c r z ∣ ∣$
$= - 8 \times 2 = - 16$

Q. Let A=⎣⎡​apx​bqy​crz​⎦⎤​ and suppose that det.(A)=2 then the det.(B) equals, where B=⎣⎡​4x4y4z​2a2b2c​−p−q−r​⎦⎤​

det(B)=−2

det(B)=−8

det(B)=−16

det(B)=8