` " if " |{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|` then the value of `k` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

we have
`|{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|`
`" or " |{:(2(a+b+c),,c+a,,a+b),(2(a+b+c),,b+c,,c+a),(2(a+b+c),,a+b,,b+c):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|`
`"[Applying " C_(1) to C_(1)+(C_(2)+C_(3)) " on " L.H.S"]"`
`" or " 2|{:(a+b+c,,-b,,-c),(a+b+c,,-a,,-b),(a+b+c,,-c,,-a):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|`
`"[Applying" C_(2) to C_(2) -C_(1),C_(3) to C_(3)-C_(1)" on " L.H.S "]"`
`" or " |{:(a,,-b,,-c),(c,,-a,,-b),(b,,-c,,-a):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|`
`"[Applying" C_(1) to C_(1) +C_(2) +C_(3) " on " L.H.S "]"`
`" or " 2|{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|=k |{:(a,,b,,c),(c,,a,,b),(b,,c,,a):}|`
`:. k=2`