Let A=`[[-5,-8,-7],[3,5,4],[2,3,3]]` and B=`[[x],[y],[2]]`.If AB is a scalar multiple of B, then the value of x + y is :
| A. |
-1 |
| B. |
-2 |
 |
| C. |
1 |
| D. |
2 |
AB =`lambda`B, where `lambda` is non-zero scalar.
`[[-5x-8y-7],[3x+5y+4],[2x+3y+3]]=lambda[[x],[y],[z]]`
i.e., –5x – 8y – 7 =`lambda`x ........(1)
3x + 5y + 4 =`lambda`y ........(2)
2x + 3y + 3 = 2`lambda` .........(3)
Addint (1), (2) and (3), we get 0 =`lambda`(x + y + 2) Since,`lambda !=0`,
x + y =0
`=>x + y = –2`