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If the system of linear equations x+a...

If the system of linear equations `x+a y+a z=0,\ x+b y+b z=0,\ x+c y+c z=0` has a non zero solution then System is always non trivial solutions System is consistent only when `a=b=c` If `a!=b!=c` then `x=0,\ y=t ,\ z=-t\ AAt in R` If `a=b=c\ t h e n\ y=t_1, z=t_2,\ x=-a(t_1+t_2)AAt_1, t_2 in R`

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ALLEN -DETERMINANTS-All Questions
  1. If |{:(a, a, x), (m, m, m),(b, x, b):}|=0,\ then x may be equal to- ...

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  2. The value of the determinant {:|(alpha,beta,l), (alpha,x, n),(alpha,be...

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  3. If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y...

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  4. If the system of equations x+y-3=0,\ (1+K)x+(2+K)y-8=0\ &\ x-(1+K)y...

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  5. If the determinant |[a+p, l+x, u+f], [b+q, x+y, v+g], [c+r, n+z, w+h]|...

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  6. The values of lambda for which the system of equations x+y+z=6,x+2y+3z...

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  7. If x , y , z are in A.P. , then the value of the determinant are in A....

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  8. Let p be the sum of all possible determinabnts of order 2 having 0,...

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  9. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  10. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  11. Statement 1 is True: Statement 2 is True; Statement 2 is a correct e...

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  12. Without expanding the determinant prove that: {:|(0,p-q,p-r),( q-p,0, ...

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  13. Without expanding the determinant prove that: {:|(0,a,-b),(-a,0,-c),(...

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  14. Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]|=|[a,b,c],[x,y,z],[yz,...

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  15. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  16. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

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  17. Using properties of determinants or otherwise evaluate {:|(18, 40, 8...

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  18. Using the property of determinants andd without expanding in following...

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  19. Using the properties of determinants, prove the following |{:(a,b-c,...

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  20. Absolute value of sum of roots of the equation {:|(x+2,2x+3,3x+4), (2x...

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