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Based on the Type of Solvent

What is trivi...

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What is trivial solution and non-trivial solution?

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Q. For a non-trivial solution

| A |

Q. Find the real values of r which the following system of linear equations has a non-trivial solution. Also find the non-trivial solutions:

2 r x - 2 y + 3 z = 0 x + r y + 2 z = 02 x + r z = 0

Q. The system of linear equations x + y = 0, x – y = 0, z = 0 will have

Q. Consider the system of equations:
a₁x + b₁y + c₁z = 0
a₂x + b₂y + c₂z = 0
a₃x + b₃y + c₃z = 0,
if

|\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}|

= 0, then the system has
(a) more than two solutions
(b) one trivial and one non-trivial solutions
(c) no solution
(d) only trivial solution (0, 0, 0)

Q. Let the system of lineat equations

2 x + 3 y - z = 0, 2 x + k y - 3 z = 0

2 x - y + z = 0

have non trivial non trivial solution then

\frac{x}{y} + \frac{y}{z} + z x + k

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