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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-c-b-c b-a-b-a c|` (b) `|a b c b c a c a b|` `|a c bb a cc b a|` (d) `|a a+bb+c bb+cc+a cc+a a+b|`

Answer

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Knowledge Check

  • if the system of equations (a-t)x+by +cz=0 bx+(c-t) y+az=0 cx+ay+(b-t)z=0 has non-trivial solutions then product of all possible values of t is

    A
    `|{:(a,,b,,c),(b,,c,,a),(c,,a,,b):}|`
    B
    `a+b+c`
    C
    `a^(2)+b^(2)+c^(2)`
    D
    `1`

  • The system of equations ax+by+(a alpha+ b)z=0 bx+cy+(b alpha+c)z=0 (a alpha+b)x+(balpha+c)y=0 has a non zero solutions if a,b,c are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    A.G.P

  • The system of linear equations x + y + z = 0 (2x)/(a) + (3y)/(b) + (4z)/(c ) = 0 (x)/(a) + (y)/(b) + (z)/(c ) = 0 has non trivia solution then

    A
    a + b + c = 0
    B
    a, b, c are in GP
    C
    `(1)/(a), (1)/(b), (1)/(c )` are in AP
    D
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