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Find the real values of r for which the ...

Find the real values of r for which the following system of linear equations has a non-trivial solu- tions. Also find the non-trivial solutions
`2rx – 2y + 3z = 0`
`x + r y + 2z = 0`
`2x + r z = 0`

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MOTION-DETERMINANTS -EXERCISE-3
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  2. Solve for x the equation |(a^(2),a,1),(sin(n+1)x,sin nx,sin(n-1)x),(...

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  3. Solve the following sets of equations using Cramer's rule and remark a...

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  4. Solve the following sets of equation using Cramers rule and remark a...

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  5. Solve the following sets of equation using Cramers rule and remark a...

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  6. For what value of K do the following system of equations poss...

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  7. Investigate for what values of lambda, mu the simultaneous equa...

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  8. Investigate for what values of lambda, mu the simultaneous equa...

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  9. . For what values of lambda and mu the system of equations x+y+z=6, x+...

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  10. If the system of equations x – ky – z = 0, kx – y – z=0, x + y – z = 0...

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  11. Find the real values of r for which the following system of linear equ...

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  12. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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  13. Ifthe equations a(y +z) =x , b(z+x) = y , c (x + y) = z have nontriv...

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  14. Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz ...

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  15. If sinq!=cosq and x,y,z satisfies the following three equations then f...

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  16. If f(x)=|(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)...

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  17. Prove that all values of theta: |(sintheta, costheta, sin2theta),(sin(...

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  18. Consider the system of equations {:(2x+lambday+6z=8),(x+2y+muz=5),(x...

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  19. Consider the system of equations 2x+lambday+6z=8 x+2y+muz=5 x+y+...

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  20. Consider the system of equations {:(2x+lambday+6z=8),(x+2y+muz=5),(x...

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