There are two possible values of A in the solution of the
matrix equation `[[2A+1,-5],[-4,A]]^(-1) [[A-5,B],[2A-2,C]]= [[14,D],[E,F]]`,
where A, B, C, D, E, F are real numbers. The absolute
value of the difference of these two solutions, is

Options

A. `8/3`
B. `11/3`
C. `1/3`
D. `19/3`

Answer

D

Explanation

`because [[A-5,B],[2A-2,C]]= [[2A+1,-5],[-4,A]][[14,D],[E,F]]`
`rArr A-5 = 28 A + 14 - 5E`
`rArr 5e = 27 A + 19` …(i)
`2A - 2 = -56 + AE`
` rArr AE = 2A +54 ` (ii)
From eq. (i), we get
`5AE = 27A^(2) + 19A`
`rArr 5 (2A+54)=27 A^(2) + 19A ` [from Eq. (ii) ]
`rArr 27A^(2) + 9 A - 270 = 0`
`rArr 9 (A-3) (3A+10)=0`
`therefore A= 3, A= -10/3`
`therefore` Absolute value of difference
`=abs(3+10/3 ) = 19/3`