If `[{:(x,-3,1),(y,1,i),(0,2i,-i):}]=6+11i,` then what are the value of x and y respectively ?

Options

A. `-3,4`
B. `3,4`
C. `3,-4`
D. `-3,-4`

Answer

A

Explanation

`[{:(x,-3i,1),(y,1,i),(0,3i,-i):}]=6+11i`
`impliesx(-i-92i)(i0-y[(-3i)(-i)-(2i)(1)]+0=6+11i`
`impliesx(-i+2)-y(-3-2i)=6+11i`
`implies-x i+2x+3y+2yi=6+11i`
`implies(2x+3y)+(-x+2y)i=6+11i`
`therefore2x+3y=6and -x2y=11`
Solving the equations,
`{:(2cancel(x)+3y=6),(-2cancelx+4y=22),(ulbar(" "7y=28 rArr y=4)):}`
`2x+3y=6implies2x+12=6`
`implies2x=-6impliesx=-3`
`thereforex=-3,y=4`