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The product of all values of t , for whi...

The product of all values of `t ,` for which the system of equations `(a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0` has non-trivial solution, is (a) `|[a, -c, -b], [-c, b, -a], [-b, -a, c]|` (b) `|[a, b, c], [b, c, a], [c, a, b]|` (c) `|[a, c, b], [b, a, c], [c, b, a]|` (d) `|[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|`

A

`|{:(a,-c,-b),(-c,b,-a),(-b,-a,c):}|`

B

`|{:(a,b,c),(b,c,a),(c,a,b):}|`

C

`|{:(a,c,b),(b,a,c),(c,b,a):}|`

D

none of these

Text Solution

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The correct Answer is:
B
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