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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`because det (B) = abs((4x, 2a, -p),(4y, 2b, -q),(4z, 2c, -r)) = -8 abs((x,a,p),(y,b,q),(z,c,r))`
`= -8 abs((x,y,z),(a,b,c),(p,q,r))= 8 abs((a,b,c),(x,y,z),(p,q,r))` [by property]
`= -8 abs((a,b,c),(p,q,r),(x,y,z)) =-8 det (A) = -16`

4 views Answered 2023-02-05 15:29