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Consider the following linear equations ...

Consider the following linear equations
`ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0`

Text Solution

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The correct Answer is:
`a rarrr,brarrq,crarrp,drarrs`
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Consider the linear equations ax +by+cz=0,bx+cy+az=0 and cx+ay+bz=0

Solve the following linear equations: ax + by = c bx + ay = 1+c

Knowledge Check

  • If agtbgtc and the system of equations ax+by+cz=0, bx+cy+az=0, cx+ay+bz=0 has a non-trivial solution, then both the roots of the quadratic equation at^(2)+bt+c=0 are

    A
    non-real
    B
    of opposite sign
    C
    positive
    D
    complex

  • If a gt b gt c and the system of equtions ax +by +cz =0,n bx +cy+az=0,cx+ay+bz=0 has a non-trivial solution then both the roots of the equadratic equation at^(2)+bt+c are

    A
    real
    B
    of opposite sign
    C
    positive
    D
    complex

  • If a+b+c =0 and a^(2)+b^(2)+c^(2)-ab-bc -ca ne 0, AA a, b, c in R then the system of equations ax+by+cz=0, bx +cy+az=0 and cx+ay+bz=0 has

    A
    A unique solution
    B
    Infinte solutions
    C
    No solution
    D
    Exactly two solutions

    • Similar Questions

    Explore conceptually related problems

    If a,b,c in R and a+b+c=0 and th esystem of equations ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0 has a non-zero solution,then a:b:c is given by

    Consider the system of equations ax+y+bz=0, bx+y+az=0 and ax+by+abz=0 where a, b in {0, 1, 2, 3, 4} . The number of ordered pairs (a, b) for which the system has non - trivial solutions is

    STATEMENT-1: If a,b,c are distinct and x,y,z are not all zero and ax+by+cz=0,bx+cy+az=0,cx+ay+bz=0, then a+b+c=0 and STATEMENT-2: a^(2)+b^(2)+c^(2)>ab+bc+ca, if a,b,c are distinct.

    If the system of linear equations ax+by+cz=0 cx+ay+bz=0 bx+cy+az=0 where a,b,c in R are non-zero and distinct , has a non-zero solution, then :

    If the system of linear equations ax +by+ cz =0 cx + cy + bz =0 bx + cy +az =0 where a,b,c, in R are non-zero and distinct, has a non-zero solution, then:

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