Value of `|x+y z z x y+z x y y z+x|,w h e r ex ,y ,z` are nonzero real number, is equal to `x y z` b. `2x y z` c. `3x y z` d. `4x y z`

Options

A. xyz
B. 2xyz
C. 3xyz
D. 4xyz

Answer

D

Explanation

Applying `R_(1) to R_(1) -(R_(2) +R_(3))` we get
`D = |{:(0,,-2y,,-2x),(x,,y+z,,x),(y,,y,,z+x):}| `
`=2|{:(0,,-y,,-x),(x,,y+z,,x),(y,,y,,z+x):}|`
`=2 |{:(0,,-y,,-x),(x,,z,,0),(y,,0,,z):}|" " underset(R_(3) to R_(3) +R_(1))((R_(2) to R_(2)+R_(1) " and "))`
`=4xyz`